Solve (x^2+5x)^2

$$( x ^ { 2 } + 5 x ) ^ { 2 }$$

Evaluate

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

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x^{2}+5x\right)^{2}.

$$\left(x^{2}\right)^{2}+10x^{2}x+25x^{2}$$

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

$$x^{4}+10x^{2}x+25x^{2}$$

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

$$x^{4}+10x^{3}+25x^{2}$$

Expand

$$x^{4}+10x^{3}+25x^{2}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x^{2}+5x\right)^{2}.

$$\left(x^{2}\right)^{2}+10x^{2}x+25x^{2}$$

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

$$x^{4}+10x^{2}x+25x^{2}$$

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

$$x^{4}+10x^{3}+25x^{2}$$