Solve left(-4x^2-8xright)^2

$${ \left(-4 { x }^{ 2 } -8x \right) }^{ 2 }$$

Evaluate

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

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(-4x^{2}-8x\right)^{2}.

$$16\left(x^{2}\right)^{2}+64x^{2}x+64x^{2}$$

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

$$16x^{4}+64x^{2}x+64x^{2}$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$16x^{4}+64x^{3}+64x^{2}$$

Expand

$$16x^{4}+64x^{3}+64x^{2}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(-4x^{2}-8x\right)^{2}.

$$16\left(x^{2}\right)^{2}+64x^{2}x+64x^{2}$$

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

$$16x^{4}+64x^{2}x+64x^{2}$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$16x^{4}+64x^{3}+64x^{2}$$