Solve (x^2+4x)^2

$$( x ^ { 2 } + 4 x ) ^ { 2 }$$

Evaluate

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

Solution Steps

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

$$\left(x^{2}\right)^{2}+8x^{2}x+16x^{2}$$

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

$$x^{4}+8x^{2}x+16x^{2}$$

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

$$x^{4}+8x^{3}+16x^{2}$$

Expand

$$x^{4}+8x^{3}+16x^{2}$$

Solution Steps

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

$$\left(x^{2}\right)^{2}+8x^{2}x+16x^{2}$$

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

$$x^{4}+8x^{2}x+16x^{2}$$

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

$$x^{4}+8x^{3}+16x^{2}$$