Solve 7x(x-5)^2-8x(2x+5)

$$7 x ( x - 5 ) ^ { 2 } - 8 x ( 2 x + 5 )$$

Evaluate

$$x\left(7x^{2}-86x+135\right)$$

Solution Steps

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

$$7x\left(x^{2}-10x+25\right)-8x\left(2x+5\right)$$

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

$$7x^{3}-70x^{2}+175x-8x\left(2x+5\right)$$

Use the distributive property to multiply -8x by 2x+5.

$$7x^{3}-70x^{2}+175x-16x^{2}-40x$$

Combine -70x^{2} and -16x^{2} to get -86x^{2}.

$$7x^{3}-86x^{2}+175x-40x$$

Combine 175x and -40x to get 135x.

$$7x^{3}-86x^{2}+135x$$

Expand

$$7x^{3}-86x^{2}+135x$$

Solution Steps

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

$$7x\left(x^{2}-10x+25\right)-8x\left(2x+5\right)$$

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

$$7x^{3}-70x^{2}+175x-8x\left(2x+5\right)$$

Use the distributive property to multiply -8x by 2x+5.

$$7x^{3}-70x^{2}+175x-16x^{2}-40x$$

Combine -70x^{2} and -16x^{2} to get -86x^{2}.

$$7x^{3}-86x^{2}+175x-40x$$

Combine 175x and -40x to get 135x.

$$7x^{3}-86x^{2}+135x$$