Solve f(x)=(2x+5)^2(3x+8)^3

$$f ( x ) = ( 2 x + 5 ) ^ { 2 } ( 3 x + 8 ) ^ { 3 }$$

Evaluate

$$\left(2x+5\right)^{2}\left(3x+8\right)^{3}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2x+5\right)^{2}.

$$\left(4x^{2}+20x+25\right)\left(3x+8\right)^{3}$$

Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(3x+8\right)^{3}.

$$\left(4x^{2}+20x+25\right)\left(27x^{3}+216x^{2}+576x+512\right)$$

Use the distributive property to multiply 4x^{2}+20x+25 by 27x^{3}+216x^{2}+576x+512 and combine like terms.

$$108x^{5}+1404x^{4}+7299x^{3}+18968x^{2}+24640x+12800$$

Expand

$$108x^{5}+1404x^{4}+7299x^{3}+18968x^{2}+24640x+12800$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2x+5\right)^{2}.

$$\left(4x^{2}+20x+25\right)\left(3x+8\right)^{3}$$

Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(3x+8\right)^{3}.

$$\left(4x^{2}+20x+25\right)\left(27x^{3}+216x^{2}+576x+512\right)$$

Use the distributive property to multiply 4x^{2}+20x+25 by 27x^{3}+216x^{2}+576x+512 and combine like terms.

$$108x^{5}+1404x^{4}+7299x^{3}+18968x^{2}+24640x+12800$$