Solve f(x)=2x(4x^2-10)^2

$$f ( x ) = 2 x ( 4 x ^ { 2 } - 10 ) ^ { 2 }$$

Evaluate

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

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(4x^{2}-10\right)^{2}.

$$2x\left(16\left(x^{2}\right)^{2}-80x^{2}+100\right)$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$2x\left(16x^{4}-80x^{2}+100\right)$$

Use the distributive property to multiply 2x by 16x^{4}-80x^{2}+100.

$$32x^{5}-160x^{3}+200x$$

Expand

$$32x^{5}-160x^{3}+200x$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(4x^{2}-10\right)^{2}.

$$2x\left(16\left(x^{2}\right)^{2}-80x^{2}+100\right)$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$2x\left(16x^{4}-80x^{2}+100\right)$$

Use the distributive property to multiply 2x by 16x^{4}-80x^{2}+100.

$$32x^{5}-160x^{3}+200x$$