Solve f(x)=x^3(x-4)*(2x+7)(2x-7)

$$f ( x ) = x ^ { 3 } ( x - 4 ) \cdot ( 2 x + 7 ) ( 2 x - 7 )$$

Evaluate

$$\left(x-4\right)\left(4x^{2}-49\right)x^{3}$$

Solution Steps

Use the distributive property to multiply x^{3} by x-4.

$$\left(x^{4}-4x^{3}\right)\left(2x+7\right)\left(2x-7\right)$$

Use the distributive property to multiply x^{4}-4x^{3} by 2x+7 and combine like terms.

$$\left(2x^{5}-x^{4}-28x^{3}\right)\left(2x-7\right)$$

Use the distributive property to multiply 2x^{5}-x^{4}-28x^{3} by 2x-7 and combine like terms.

$$4x^{6}-16x^{5}-49x^{4}+196x^{3}$$

Expand

$$4x^{6}-16x^{5}-49x^{4}+196x^{3}$$

Solution Steps

Use the distributive property to multiply x^{3} by x-4.

$$\left(x^{4}-4x^{3}\right)\left(2x+7\right)\left(2x-7\right)$$

Use the distributive property to multiply x^{4}-4x^{3} by 2x+7 and combine like terms.

$$\left(2x^{5}-x^{4}-28x^{3}\right)\left(2x-7\right)$$

Use the distributive property to multiply 2x^{5}-x^{4}-28x^{3} by 2x-7 and combine like terms.

$$4x^{6}-16x^{5}-49x^{4}+196x^{3}$$