{"id":927,"date":"2025-10-15T12:38:45","date_gmt":"2025-10-15T12:38:45","guid":{"rendered":"https:\/\/kapdec.com\/help\/?post_type=docs&#038;p=927"},"modified":"2026-04-09T12:12:59","modified_gmt":"2026-04-09T12:12:59","slug":"what-are-algebraic-expressions","status":"publish","type":"post","link":"https:\/\/kapdec.com\/help\/what-are-algebraic-expressions\/","title":{"rendered":"What are Algebraic Expressions?"},"content":{"rendered":"<p><strong>Algebraic Expressions\u00a0Introduction:\u00a0\u00a0<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p>An\u00a0<b>operator<\/b>\u00a0is a symbol that shows a\u00a0mathematical\u00a0operation.<\/p>\n<p>For\u00a0<b>example,\u00a0the symbols,\u00a0<\/b>\u201c<b>+<\/b>\u201d, \u201c<b>-\u201d,<\/b>\u00a0\u201c<b>*<\/b>\u201d, \u201c<b>\/\u201d<\/b>\u00a0;\u00a0describe what we want to do with the values, wherever above symbols are present.<\/p>\n<p>&nbsp;<\/p>\n<p>A\u00a0<b>term<\/b>\u00a0is either a variable or a single number, or variables and numbers multiplied together.<\/p>\n<p>For\u00a0<b>example:<\/b>\u00a0X, 2X, 3Y or 5.<\/p>\n<p>&nbsp;<\/p>\n<p>When an operator is put in between two terms, it becomes expression. So,\u00a0<b>expression<\/b>\u00a0is defined as group of terms separated by operator.<\/p>\n<p>&nbsp;<\/p>\n<p><b>3 X- 8 is an expression.\u00a0<\/b><\/p>\n<p>&nbsp;<\/p>\n<p>Expressions can be formed by numbers as well as\u00a0(instead of\u00a0variables)<\/p>\n<p>In case of forming expression using only numbers,\u00e0\u00a05 + (6\u00a0&#8211;\u00a03)<\/p>\n<p>In case of forming expression using variables and numbers,\u00a0then we have<\/p>\n<p>5 m + 9<\/p>\n<p>&nbsp;<\/p>\n<p>Such expressions where both constants and variables are included are called\u00a0<b>algebraic expressions.<\/b><\/p>\n<p><b>Example:<\/b><\/p>\n<p>3x + 2y &#8211; 5z= 10. What is expression and terms here?<\/p>\n<p><b>Solution<\/b><\/p>\n<p>3x + 2y &#8211; 5z is an expression.<\/p>\n<p>Various terms of the expression are: 3X, 2Y, 5Z, 10<\/p>\n<p>&nbsp;<\/p>\n<p><b>Note:<\/b><\/p>\n<ul>\n<li>The expression\u00a0containing\u00a0only one term is called\u00a0<b>monomial<\/b>.<\/li>\n<\/ul>\n<p><b>Example:\u00a0<\/b>5x<\/p>\n<ul>\n<li>The expression\u00a0having\u00a0two terms is called\u00a0<b>binomial<\/b>.<\/li>\n<\/ul>\n<p><b>Example:<\/b>\u00a05x + 10<\/p>\n<ul>\n<li>The expression\u00a0containing\u00a0three terms is called\u00a0<b>trinomial<\/b>.<br \/>\n<b>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Example:<\/b>\u00a02a + 3b &#8211; 4<\/li>\n<\/ul>\n<ul>\n<li>The expression containing\u00a0more than three terms is called\u00a0<b>polynomial\u00a0<\/b>as there is no special name for expressions containing more than three terms.<\/li>\n<\/ul>\n<p><b>Example:<\/b>3x + 4y \u2013 8z + 7<\/p>\n<ul>\n<li>All monomials, binomials and trinomials are\u00a0ALSO\u00a0polynomials.<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>Value of an Algebraic Expression:<\/p>\n<p>If we assign values to the symbols or letters of algebraic expression then we can calculate the value of an algebraic expression.<\/p>\n<p>Let us understand the concept by following\u00a0<b>example<\/b>:<\/p>\n<p>If\u00a0<b>a<\/b>\u00a0=6,\u00a0<b>b<\/b>= 7 and\u00a0<b>c<\/b>=8. Calculate the value of\u00a0<b>a\u00a0+ b- c.<\/b><\/p>\n<p>By putting given values of a, b and c in the algebraic expression: (a+ b- c), we get 6+ 7 -8 This is equal to 5.\u00a0So\u00a0the value of given algebraic expression (a +b- c) is 5.<\/p>\n<p>&nbsp;<\/p>\n<p><b>Example:\u00a0<\/b>Calculate the value of algebraic expression:<\/p>\n<p>(10x+ 3y- 4)\u00a0if x=2 and y=1<\/p>\n<p>&nbsp;<\/p>\n<p><b>Solution<\/b><\/p>\n<p>The given algebraic expression is (10x + 3y- 4)<\/p>\n<p>By putting the respective values of (x=2) and (y=1) in the algebraic expression, we get<\/p>\n<p>= (10 \u00d7 2) + (3 \u00d7 1) &#8211; 4<\/p>\n<p>After solving parenthesis, we get<\/p>\n<p>=20 + 3 \u2013 4<\/p>\n<p>=19<\/p>\n<p>&nbsp;<\/p>\n<p><b>Example 12:\u00a0<\/b>Evaluate the algebraic expression: 3x+ (13-y) &#8211; 4z.\u00a0If x=2, y=4, z=3<\/p>\n<p>&nbsp;<\/p>\n<p><b>Solution:<\/b><\/p>\n<p>The given algebraic expression is 3x+ (13-y) &#8211; 4z<\/p>\n<p>By putting the respective values of (x=2), (y=4) and (z=3)<\/p>\n<p>in the algebraic expression, we get<\/p>\n<p>= (3* 2) + (13 -4) \u2013 (4*3)<\/p>\n<p>After solving parenthesis we get<\/p>\n<p>=6 + 9 \u2013 12<\/p>\n<p>=3<\/p>\n<p>So,\u00a0the value of expression is 3.<\/p>\n<p>&nbsp;<\/p>\n<p>Like and Unlike Terms<\/p>\n<p>The terms whose variables are same are called\u00a0<b>like terms.<\/b><\/p>\n<p>For\u00a0<b>example<\/b>, 10x,\u00a02x,\u00a04x. All these terms have x and same power of x. So these terms can be easily added and subtracted like 10x + 2x +4x =16x.<\/p>\n<p>Compare this to the above situation &#8211; Yasin bought 10 eggs,\u00a0Samy\u00a0bought 2 eggs and\u00a0Amna\u00a0bought 4 eggs. So, all three, together, have bought the same\/like item which is egg.\u00a0 Hence it can be added. It was easier to write eggs in place of x.<\/p>\n<p><b>Unlike terms<\/b>\u00a0are those terms which have different variables.<\/p>\n<p>For\u00a0<b>example<\/b>, 10x and 4y. These two terms have two different variables, therefore those are unlike terms. It can be understood such as in following example,\u00a0ie, 10 oranges and 4 apples are not like quantity.\u00a0So\u00a0for all future reference when one or more terms in an algebraic expressions have completely different variables, then they are called unlike terms.<\/p>\n<p>&nbsp;<\/p>\n<p><b>Example:<\/b><\/p>\n<p>State whether following pair of terms are like or unlike terms?<\/p>\n<ul>\n<li>11mn, 13mn<\/li>\n<\/ul>\n<ul>\n<li>-3x,x<\/li>\n<li>4xy + 2yx<\/li>\n<li>5ab + 6b<\/li>\n<\/ul>\n<p><b>Solution<\/b><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-928\" src=\"https:\/\/kapdec.com\/help\/venture\/wp-content\/uploads\/2025\/10\/blob-2-2-300x124.png\" alt=\"\" width=\"300\" height=\"124\" \/><\/p>\n<p><b>Did You Know?<\/b><\/p>\n<p>Basketball has a strong association with Algebra. Davidson College associate math professor Tim\u00a0Chartier\u00a0developed algebraic formulas for the NCAA basketball tournament. Even the famous NBA<br \/>\n24-second shot clock was also created using an algebraic equation.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Algebraic Expressions\u00a0Introduction:\u00a0\u00a0 &nbsp; An\u00a0operator\u00a0is a symbol that shows a\u00a0mathematical\u00a0operation. For\u00a0example,\u00a0the symbols,\u00a0\u201c+\u201d, \u201c-\u201d,\u00a0\u201c*\u201d, \u201c\/\u201d\u00a0;\u00a0describe what we want to do with the values, wherever above symbols are present. &nbsp; A\u00a0term\u00a0is either a variable or a single number, or variables and numbers multiplied together. For\u00a0example:\u00a0X, 2X, 3Y or 5. &nbsp; When an operator is put in between two [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[590],"tags":[603,595],"class_list":["post-927","post","type-post","status-publish","format-standard","hentry","category-grade-5","tag-algebra","tag-grade-5-mathematics"],"_links":{"self":[{"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/posts\/927","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/comments?post=927"}],"version-history":[{"count":1,"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/posts\/927\/revisions"}],"predecessor-version":[{"id":1522,"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/posts\/927\/revisions\/1522"}],"wp:attachment":[{"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/media?parent=927"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/categories?post=927"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/tags?post=927"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}