# Expand  `(3x + 2)^2 (2x+3)^3` (3x+2)^2(2x+3)^3

Asked on by kikinc4

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

You may expand the square of binomial `3x+2`  using the formula such that:

`(a+b)^2 = a^2 + 2ab + b^2`

Reasoning by analogy yields:

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

`(3x+2)^2 = 9x^2 + 12x + 4`

You may expand the cube of binomial `2x+3`  using the formula such that:

`(a+b)^3 = a^3 + b^3 + 3ab(a+b)`

Reasoning by analogy yields:

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

`(2x+3)^3 = 8x^3 +27 + 18x(2x+3)`

Evaluating the product `(3x+2)^2(2x+3)^3`  such that:

`(3x+2)^2(2x+3)^3 = (9x^2 + 12x + 4)(8x^3 + 27 + 18x(2x+3)) `

`(3x+2)^2(2x+3)^3 = 9x^2*8x^3 + 9*27x^2 + 9x^2*18x(2x+3) + 12*8x^3 + 12x*27 + 12x*18x(2x+3) + 4*8x^3 + 4*27 + 4*18x(2x+3)`

`(3x+2)^2(2x+3)^3 = 72x^5 + 243x^2 + 162x^3(2x+3) + 96x^3 + 324x + 216x^2(2x+3) + 32x^3 +108 + 72x(2x+3)`

`(3x+2)^2(2x+3)^3 = 72x^5 + 243x^2 + 324x^4 + 582x^3 + 324x + 432x^3 + 648x^2 + 32x^3 + 108 + 144x^2 + 216x`

`(3x+2)^2(2x+3)^3 = 72x^5+ 324x^4 + 1046x^3 + 1035x^2 + 540x + 108`

Hence, expanding the binomials yields `(3x+2)^2(2x+3)^3 = 72x^5 + 324x^4 + 1046x^3 + 1035x^2 + 540x + 108.`

senthuraan | Student, Grade 10 | (Level 3) eNoter

Posted on

(3x+2)(3x+2)  &  (2x+3)(2x+3)

so that you seperate these and try, lets do like this..

3x(3x+2)+2(3x+2) & 2x(2x+3)+3(2X+3)

9X^2+6x+4 & 4x^2+6x+6X+9

lets remove the ''&'' and mix it.. concentrate when joining them and carefully try this...

9X^2+6x+4*4x^2+6x+6X+9

9x^2+4x^2+18x+13

ahhhhhhhhhh! this is the ANSWER :')

ANYONE TELL IF I MADE ANY MISTAKE!

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