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Use special products to expand and simplify: 5x^m(x^(m+1) + 3)^2Show solution and...

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spock8 | Student, Undergraduate | (Level 1) Honors

Posted April 27, 2012 at 1:19 PM via web

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Use special products to expand and simplify: 5x^m(x^(m+1) + 3)^2

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted April 27, 2012 at 1:37 PM (Answer #1)

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You need to expand binomial `(x^(m+1) + 3)^2`  using the formula `(a+b)^2 = a^2 + 2ab + b^2`  such that:

`(x^(m+1) + 3)^2 = (x^(m+1))^2 + 2*3*x^(m+1) + 3^2`

`(x^(m+1) + 3)^2 = (x^(2m+2)) + 6x^(m+1) + 9`

You need to multiply the expanded binomial by `5x^m`  such that:

`5x^m*(x^(m+1) + 3)^2 = 5(x^m*x^(2m+2)) + 30x^m*x^(m+1) + 45x^m`

`5x^m*(x^(m+1) + 3)^2 = 5(x^(m+2m+2)) + 30x^(m+m+1) + 45x^m`

`5x^m*(x^(m+1) + 3)^2 = 5(x^(3m+2)) + 30x^(2m+1) + 45x^m`

Hence, simplifying the product yields  `5x^m*(x^(m+1) + 3)^2 = 5(x^(3m+2)) + 30x^(2m+1) + 45x^m` .

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