Solve w=10+10(x-7)^2(x-4)

$$w = 10 + 10 ( x - 7 ) ^ { 2 } ( x - 4 )$$

Solve for w

$$w=10\left(\left(x-4\right)\left(x-7\right)^{2}+1\right)$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-7\right)^{2}.

$$w=10+10\left(x^{2}-14x+49\right)\left(x-4\right)$$

Use the distributive property to multiply 10 by x^{2}-14x+49.

$$w=10+\left(10x^{2}-140x+490\right)\left(x-4\right)$$

Use the distributive property to multiply 10x^{2}-140x+490 by x-4 and combine like terms.

$$w=10+10x^{3}-180x^{2}+1050x-1960$$

Subtract 1960 from 10 to get -1950.

$$w=-1950+10x^{3}-180x^{2}+1050x$$