Solve (x^2+5x)^2-12(x^2+5x)+36

$$( x ^ { 2 } + 5 x ) ^ { 2 } - 12 ( x ^ { 2 } + 5 x ) + 36$$

Evaluate

$$\left(\left(x-1\right)\left(x+6\right)\right)^{2}$$

Solution Steps

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

$$\left(x^{2}\right)^{2}+10x^{2}x+25x^{2}-12\left(x^{2}+5x\right)+36$$

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

$$x^{4}+10x^{2}x+25x^{2}-12\left(x^{2}+5x\right)+36$$

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

$$x^{4}+10x^{3}+25x^{2}-12\left(x^{2}+5x\right)+36$$

Use the distributive property to multiply -12 by x^{2}+5x.

$$x^{4}+10x^{3}+25x^{2}-12x^{2}-60x+36$$

Combine 25x^{2} and -12x^{2} to get 13x^{2}.

$$x^{4}+10x^{3}+13x^{2}-60x+36$$

Expand

$$x^{4}+10x^{3}+13x^{2}-60x+36$$

Solution Steps

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

$$\left(x^{2}\right)^{2}+10x^{2}x+25x^{2}-12\left(x^{2}+5x\right)+36$$

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

$$x^{4}+10x^{2}x+25x^{2}-12\left(x^{2}+5x\right)+36$$

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

$$x^{4}+10x^{3}+25x^{2}-12\left(x^{2}+5x\right)+36$$

Use the distributive property to multiply -12 by x^{2}+5x.

$$x^{4}+10x^{3}+25x^{2}-12x^{2}-60x+36$$

Combine 25x^{2} and -12x^{2} to get 13x^{2}.

$$x^{4}+10x^{3}+13x^{2}-60x+36$$