In this article, we are going to introduce a new concept that is Cube of the Sum of Two Binomials terms. We are providing the different problems with a clear explanation on this topic. Follow our page and get full of knowledge on it. Firstly, to find the cube of the sum of two binomials, we need to multiply the binomials term three times. Refer to Solved Examples on Cube of Sum of Two Binomials provided along with Solutions for better understanding of the concept.<\/p>\n
For example, (x + y) ^3 = (x + y) (x + y)^2 is the example of a binomial expression.<\/p>\n
Here, we have an equation in an algebra like (a + b)^2 = a^2 + 2ab + b^2.
\nBy using the above equation, we can expand the cube term.
\n(x + y) (x + y)^2 = (x + y) (x^2 + 2xy + y^2).
\nMultiply the terms (x + y) and (x^2 + 2xy + y^2). Then we get
\n(x + y) (x^2 + 2xy + y^2) = x (x^2 + 2xy + y^2) + y (x^2 + 2xy + y^2).
\n= x^3 + 2x^2y + xy^2 + yx^2 + 2xy^2 + y^3.
\n= x^3 + 3x^2y + 3xy^2 + y^3.
\n= x^3 +y^3 + 3xy(x + y).<\/p>\n
Also, Read: Cube of a Binomial<\/a><\/p>\n 1. Determine the expansion of (x + 2y)^3.<\/strong><\/p>\n Solution: Therefore, (x + 2y)^3 is equal to x^3 + 8y^3 + 6x^2y + 12xy^2.<\/p>\n 2. Evaluate (55)^3.<\/strong><\/p>\n Solution: Therefore, (55)^3 is equal to 1,66,375.<\/p>\n 3. Find the value of 64x^3 + y^3 if 4x + y = 6 and xy = 5.<\/strong><\/p>\n Solution: Therefore, 64x^3 + y^3 is equal to -144.<\/p>\n 4. If a + 1\/a = 3, find the values of a^3 \u2013 1\/a^3.<\/strong><\/p>\n Solution: Therefore, a^3 + 1\/a^3 is equal to 18.<\/p>\n 5. Expand the term (2x + y)^3.<\/strong><\/p>\n Solution: The final answer is 8x^3 + y^3 + 12x^2y + 6xy^2.<\/p>\n","protected":false},"excerpt":{"rendered":" In this article, we are going to introduce a new concept that is Cube of the Sum of Two Binomials terms. We are providing the different problems with a clear explanation on this topic. Follow our page and get full of knowledge on it. Firstly, to find the cube of the sum of two binomials, … Read more<\/a><\/p>\n","protected":false},"author":3,"featured_media":54908,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[5],"tags":[],"jetpack_featured_media_url":"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/03\/Cube-of-the-Sum-of-Two-Binomials.png","_links":{"self":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/54905"}],"collection":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/comments?post=54905"}],"version-history":[{"count":1,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/54905\/revisions"}],"predecessor-version":[{"id":92478,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/54905\/revisions\/92478"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media\/54908"}],"wp:attachment":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media?parent=54905"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/categories?post=54905"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/tags?post=54905"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Cube of Sum of Two Binomials Examples<\/h2>\n
\nThe given expression is (x + 2y)^3.
\nWe have an equation on cubes like (x + y)^3 = x^3 + y^3 + 3xy(x + y).
\nBy comparing the above expression with the (x + y)^3
\nHere, x = x and y = 2y
\nSubstitute the terms in the equation (x + y)^3
\nThat is, (x + 2y)^3 = x^3 + (2y)^3 + 3x(2y)(x + 2y).
\n= x^3 + 8y^3 + 6xy(x + 2y).
\n= x^3 + 8y^3 + 6x^2y + 12xy^2.<\/p>\n
\nThe given one is (55)^3.
\nWe can write it as (50 + 5)^3.
\n(x + y)^3 = x^3 + y^3 + 3xy(x + y).
\nBy comparing the (50 + 5)^3 with the above expression.
\nx = 50 and y = 5.
\nSubstitute the values in the expression.
\n(50 + 5)^3 = (50)^3 + (5)^3 + 3(50)(5)(50 + 5).
\n= 1,25,000 + 125 + 750(55).
\n= 1,25,000 + 125 + 41,250.
\n= 1,66,375.<\/p>\n
\nThe given expression is 64x^3 + y^3.
\n4x + y = 6.
\nCube the terms on both sides. Then, we will get
\n(4x + y)^3 = (6)^3.
\nWe have an equation (x + y)^3 = x^3 + y^3 + 3xy(x + y).
\nHere, x = 4x and y = y.
\nSubstitute the values in the equation. Then,
\n(4x)^3 + y^3 + 3(4x)(y)(4x + y) = 216.
\n64x^3 + y^3 + 12xy(4x + y) = 216.
\nBut 4x + y = 6 and xy = 5.
\nSo, 64x^3 + y^3 + 12(5)(6) = 216.
\n64x^3 + y^3 + 360 = 216.
\n64x^3 + y^3 = -144.<\/p>\n
\nThe given term is a + 1\/a = 3
\nCube the terms on both sides. Then, we will get
\n(a + 1\/a)^3 = (3)^3.
\nWe have an equation (x + y)^3 = x^3 + y^3 + 3xy(x + y).
\nBy comparing the given terms with the equation.
\nHere, x = a and y = 1\/a.
\nBy substituting the terms in the given equation. We will get
\n(a + 1\/a)^3 = a^3 + (1\/a)^3 + 3a(1\/a)(a + 1\/a) = 27.
\n= a^3 + 1\/a^3 +3(a + 1\/a) = 27.
\nWe have (a + 1\/a) = 3. By substituting this value in the above expression.
\na^3 + 1\/a^3 + 3(a + 1\/a) =27.
\na^3 + 1\/a^3 + 3(3) = 27.
\na^3 + 1\/a^3 +9 = 27.
\na^3 + 1\/a^3 = 27 \u2013 9 = 18.<\/p>\n
\nThe given expression is (2x + y)^3.
\nwe have an equation (x + y)^3 = x^3 + y^3 + 3xy(x + y).
\nby comparing the (2x + y)^3 with the above equation.
\nHere, x = 2x and y = y.
\n(2x + y)^3 = (2x)^3 + (y)^3 +3(2x)(y)(2x + y).
\n= 8x^3 + y^3 + 6xy(2x + y).
\n= 8x^3 + y^3 + 12x^2y + 6xy^2.<\/p>\n