Solve G(x)=7(x-5)^2(x^2+2)

$$G ( x ) = 7 ( x - 5 ) ^ { 2 } ( x ^ { 2 } + 2 )$$

Evaluate

$$7\left(x-5\right)^{2}\left(x^{2}+2\right)$$

Solution Steps

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

$$7\left(x^{2}-10x+25\right)\left(x^{2}+2\right)$$

Use the distributive property to multiply 7 by x^{2}-10x+25.

$$\left(7x^{2}-70x+175\right)\left(x^{2}+2\right)$$

Use the distributive property to multiply 7x^{2}-70x+175 by x^{2}+2 and combine like terms.

$$7x^{4}+189x^{2}-70x^{3}-140x+350$$

Expand

$$7x^{4}-70x^{3}+189x^{2}-140x+350$$

Solution Steps

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

$$7\left(x^{2}-10x+25\right)\left(x^{2}+2\right)$$

Use the distributive property to multiply 7 by x^{2}-10x+25.

$$\left(7x^{2}-70x+175\right)\left(x^{2}+2\right)$$

Use the distributive property to multiply 7x^{2}-70x+175 by x^{2}+2 and combine like terms.

$$7x^{4}+189x^{2}-70x^{3}-140x+350$$