Solve y=(3x-2)^2(2x+3)^3

$$y = ( 3 x - 2 ) ^ { 2 } ( 2 x + 3 ) ^ { 3 }$$

Solve for y

$$y=\left(3x-2\right)^{2}\left(2x+3\right)^{3}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(3x-2\right)^{2}.

$$y=\left(9x^{2}-12x+4\right)\left(2x+3\right)^{3}$$

Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(2x+3\right)^{3}.

$$y=\left(9x^{2}-12x+4\right)\left(8x^{3}+36x^{2}+54x+27\right)$$

Use the distributive property to multiply 9x^{2}-12x+4 by 8x^{3}+36x^{2}+54x+27 and combine like terms.

$$y=72x^{5}+228x^{4}+86x^{3}-261x^{2}-108x+108$$