{"id":124,"date":"2020-02-15T09:00:52","date_gmt":"2020-02-15T09:00:52","guid":{"rendered":"http:\/\/www.winstechnologies.com\/blog\/?p=124"},"modified":"2020-07-21T11:40:28","modified_gmt":"2020-07-21T11:40:28","slug":"algebra-formulas","status":"publish","type":"post","link":"https:\/\/www.winstechnologies.com\/blog\/algebra-formulas\/","title":{"rendered":"Algebra Formulas and Expression with Example"},"content":{"rendered":"\n<h3 class=\"wp-block-heading\">Algebra Formulas &#8211; What is Algebra?<\/h3>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"704\" height=\"1024\" src=\"https:\/\/www.winstechnologies.com\/blog\/wp-content\/uploads\/2020\/07\/a5a8795368be161444b69827196b6168-704x1024.jpg\" alt=\"Algebra Formulas\" class=\"wp-image-410\" srcset=\"https:\/\/www.winstechnologies.com\/blog\/wp-content\/uploads\/2020\/07\/a5a8795368be161444b69827196b6168-704x1024.jpg 704w, https:\/\/www.winstechnologies.com\/blog\/wp-content\/uploads\/2020\/07\/a5a8795368be161444b69827196b6168-206x300.jpg 206w, https:\/\/www.winstechnologies.com\/blog\/wp-content\/uploads\/2020\/07\/a5a8795368be161444b69827196b6168-768x1117.jpg 768w, https:\/\/www.winstechnologies.com\/blog\/wp-content\/uploads\/2020\/07\/a5a8795368be161444b69827196b6168-1056x1536.jpg 1056w, https:\/\/www.winstechnologies.com\/blog\/wp-content\/uploads\/2020\/07\/a5a8795368be161444b69827196b6168.jpg 1100w\" sizes=\"auto, (max-width: 704px) 100vw, 704px\" \/><\/figure>\n\n\n\n<p><strong>Algebra<\/strong> is basically a branch of mathematics which deals with symbols and the rules for manipulating with those symbols. <strong>Algebra<\/strong> allows you to substitute the values in order to solve the equations for the unknown quantities. <\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><a href=\"https:\/\/byjus.com\/algebra-formulas\/\" class=\"rank-math-link\" target=\"_blank\" rel=\"noopener\">Algebra Formula<\/a><\/h3>\n\n\n\n<p>Algebra Formulas represents the relationship between the different  variables. The variable can be taken as a, b, c, x, y or any other alphabet that represents a number unknown yet. <\/p>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>A list of Algebraic formulas<\/strong><\/h4>\n\n\n\n<ul class=\"wp-block-list\"><li>a<sup>2<\/sup> \u2013 b<sup>2<\/sup> = (a \u2013 b)(a + b)<\/li><li>(a+b)<sup>2<\/sup> = a<sup>2<\/sup> + 2ab + b<sup>2<\/sup><\/li><li>a<sup>2<\/sup> + b<sup>2<\/sup> = (a + b)<sup>2<\/sup>&nbsp;\u2013 2ab<\/li><li>(a \u2013 b)<sup>2<\/sup> = a<sup>2<\/sup> \u2013 2ab + b<sup>2<\/sup><\/li><li>(a + b + c)<sup>2<\/sup> = a<sup>2<\/sup> + b<sup>2<\/sup> + c<sup>2<\/sup> + 2ab + 2bc + 2ca<\/li><li>(a \u2013 b \u2013 c)<sup>2<\/sup> = a<sup>2<\/sup> + b<sup>2<\/sup> + c<sup>2<\/sup> \u2013 2ab + 2bc \u2013 2ca<\/li><li>(a + b)<sup>3<\/sup> = a<sup>3<\/sup> + 3a<sup>2<\/sup>b + 3ab<sup>2<\/sup> + b<sup>3<\/sup> ; (a + b)<sup>3<\/sup> = a<sup>3<\/sup> + b<sup>3<\/sup> + 3ab(a + b)<\/li><li>(a \u2013 b)<sup>3<\/sup> = a<sup>3<\/sup> \u2013 3a<sup>2<\/sup>b + 3ab<sup>2<\/sup> \u2013 b<sup>3<\/sup><\/li><li>a<sup>3<\/sup> \u2013 b<sup>3<\/sup> = (a \u2013 b)(a<sup>2<\/sup> + ab + b<sup>2<\/sup>)<\/li><li>a<sup>3<\/sup> + b<sup>3<\/sup> = (a + b)(a<sup>2<\/sup> \u2013 ab + b<sup>2<\/sup>)<\/li><li>(a + b)<sup>3<\/sup> = a<sup>3<\/sup> + 3a<sup>2<\/sup>b + 3ab<sup>2<\/sup> + b<sup>3<\/sup><\/li><li>(a \u2013 b)<sup>3<\/sup> = a<sup>3<\/sup> \u2013 3a<sup>2<\/sup>b + 3ab<sup>2<\/sup> \u2013 b<sup>3<\/sup><\/li><li>(a + b)<sup>4<\/sup> = a<sup>4<\/sup> + 4a<sup>3<\/sup>b + 6a<sup>2<\/sup>b<sup>2<\/sup> + 4ab<sup>3<\/sup> + b<sup>4<\/sup>)<\/li><li>(a \u2013 b)<sup>4<\/sup> = a<sup>4<\/sup> \u2013 4a<sup>3<\/sup>b + 6a<sup>2<\/sup>b<sup>2<\/sup> \u2013 4ab<sup>3<\/sup> + b<sup>4<\/sup>)<\/li><li>a<sup>4<\/sup> \u2013 b<sup>4<\/sup> = (a \u2013 b)(a + b)(a<sup>2<\/sup> + b<sup>2<\/sup>)<\/li><li>a<sup>5<\/sup> \u2013 b<sup>5<\/sup> = (a \u2013 b)(a<sup>4<\/sup> + a<sup>3<\/sup>b + a<sup>2<\/sup>b<sup>2<\/sup> + ab<sup>3<\/sup> + b<sup>4<\/sup>)<\/li><li><strong>If n is a natural number<\/strong>&nbsp;a<sup>n<\/sup> \u2013 b<sup>n<\/sup> = (a \u2013 b)(a<sup>n-1<\/sup> + a<sup>n-2<\/sup>b+\u2026+ b<sup>n-2<\/sup>a + b<sup>n-1<\/sup>)<\/li><li><strong>If n is even<\/strong> (n = 2k), a<sup>n<\/sup> + b<sup>n<\/sup> = (a + b)(a<sup>n-1<\/sup> \u2013 a<sup>n-2<\/sup>b +\u2026+ b<sup>n-2<\/sup>a \u2013 b<sup>n-1<\/sup>)<\/li><li><strong>If n is odd<\/strong> (n = 2k + 1), a<sup>n<\/sup> + b<sup>n<\/sup> = (a + b)(a<sup>n-1<\/sup> \u2013 a<sup>n-2<\/sup>b +\u2026- b<sup>n-2<\/sup>a + b<sup>n-1<\/sup>)<\/li><li>(a + b + c + \u2026)<sup>2<\/sup> = a<sup>2<\/sup> + b<sup>2<\/sup> + c<sup>2<\/sup> + \u2026 + 2(ab + ac + bc + \u2026.)<\/li><li><strong>Laws of Exponents <\/strong>(a<sup>m<\/sup>)(a<sup>n<\/sup>) = a<sup>m+n<\/sup> ; (ab)<sup>m<\/sup> = a<sup>m<\/sup>b<sup>m <\/sup>; (a<sup>m<\/sup>)<sup>n<\/sup> = a<sup>mn<\/sup><\/li><li><strong>Fractional Exponents<\/strong> a<sup>0<\/sup> = 1 ; <em>aman<\/em>=<em>am<\/em>\u2212<em>n<\/em> ; <em>am<\/em> = 1<em>a<\/em>\u2212<em>m<\/em> ; <em>a<\/em>\u2212<em>m<\/em> = 1<em>am<\/em><\/li><\/ul>\n\n\n\n<h4 class=\"wp-block-heading\"> <strong>Roots of Quadratic Equation<\/strong> <\/h4>\n\n\n\n<ul class=\"wp-block-list\"><li>For a quadratic equation ax<sup>2<\/sup> + bx + c where a \u2260 0, the roots will be given by the equation as \\[\\frac{-b\\pm \\sqrt{b^{2}-4ac}}{2a}\\]<\/li><li>\u0394 = b<sup>2<\/sup> \u2212 4ac is called the discrimination<\/li><li>For real and distinct roots, \u0394 &gt; 0<\/li><li>For real &amp; coincident roots, \u0394 = 0<\/li><li>For non-real roots, \u0394 &lt; 0<\/li><li>If \u03b1 and \u03b2 are the two roots of the equation ax<sup>2<\/sup> + bx + c then, \u03b1 + \u03b2 = (-b \/ a) and \u03b1 \u00d7 \u03b2 = (c \/ a).<\/li><li>If the roots of a quadratic equation are \u03b1 and \u03b2, the equation will be (x \u2212 \u03b1)(x \u2212 \u03b2) = 0<\/li><\/ul>\n\n\n\n<h4 class=\"wp-block-heading\"> <strong>Factorials<\/strong> <\/h4>\n\n\n\n<ul><li>n! = (1).(2).(3)\u2026..(n \u2212 1).n<\/li><li>n! = n(n \u2212 1)! = n(n \u2212 1)(n \u2212 2)! = \u2026.<\/li><li>0! = 1<\/li>\n<li>\\[\\ (a + b)^{n} = a^{n}+na^{n-1}b+\\frac{n(n-1)}{2!}a^{n-2}b^{2}+\\frac{n(n-1)(n-2)}{3!}a^{n-3}b^{3}+\u2026.+b^{n}, where\\;,n&gt;1 \\]<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\"> Algebra Problems with a Solution <\/h3>\n\n\n\n<h4 class=\"wp-block-heading\"> Solved Examples of Algebra Formulas<\/h4>\n\n\n\n<p><strong>Question&nbsp;1: <\/strong>Find out the value of 5<sup>2<\/sup> \u2013 3<sup>2<br><\/sup><strong>Solution:<\/strong><br> Using the formula&nbsp;a<sup>2<\/sup> \u2013 b<sup>2<\/sup> = (a \u2013 b)(a + b)<br> where a = 5 and b = 3<br> (a \u2013 b)(a + b)<br> = (5 \u2013 3)(5 + 3)<br> = 2&nbsp;\u00d7 8<br> = 16<br><strong><br>Question&nbsp;2: <\/strong>4<sup>3<\/sup> \u00d7 4<sup>2<\/sup> = ?<br><strong>Solution:<br> <\/strong>Using the exponential formula (a<sup>m<\/sup>)(a<sup>n<\/sup>) = a<sup>m+n<br> <\/sup>where a = 4<br> 4<sup>3<\/sup> \u00d7 4<sup>2<br> <\/sup>= 4<sup>3+2<\/sup> = 4<sup>5<\/sup> = 1024 <\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Download Algebra Formula PDF<\/strong><\/h2>\n\n\n\n<p><a alt=\"Algebra PDF\" title=\"Download Algebra Formula PDF\" target=\"_blank\" href=\"https:\/\/www.winstechnologies.com\/blog\/wp-content\/uploads\/2020\/04\/FinalFormulas.pdf\" rel=\"noopener noreferrer\">Click Here<\/a><\/p>\n\n\n\n<pre class=\"wp-block-code\"><code><\/code><\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Algebra Formulas &#8211; What is Algebra? Algebra is basically a branch of mathematics which deals with symbols and the rules for manipulating with those symbols.&#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-124","post","type-post","status-publish","format-standard","hentry","category-maths-formula","entry"],"_links":{"self":[{"href":"https:\/\/www.winstechnologies.com\/blog\/wp-json\/wp\/v2\/posts\/124","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.winstechnologies.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.winstechnologies.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.winstechnologies.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.winstechnologies.com\/blog\/wp-json\/wp\/v2\/comments?post=124"}],"version-history":[{"count":26,"href":"https:\/\/www.winstechnologies.com\/blog\/wp-json\/wp\/v2\/posts\/124\/revisions"}],"predecessor-version":[{"id":412,"href":"https:\/\/www.winstechnologies.com\/blog\/wp-json\/wp\/v2\/posts\/124\/revisions\/412"}],"wp:attachment":[{"href":"https:\/\/www.winstechnologies.com\/blog\/wp-json\/wp\/v2\/media?parent=124"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.winstechnologies.com\/blog\/wp-json\/wp\/v2\/categories?post=124"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.winstechnologies.com\/blog\/wp-json\/wp\/v2\/tags?post=124"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}