Solve (2x+5)(2x+5)-9*(x+1)(x+1)

$$( 2 x + 5 ) ( 2 x + 5 ) - 9 * ( x + 1 ) ( x + 1 )$$

Evaluate

$$\left(2-x\right)\left(5x+8\right)$$

Solution Steps

Multiply 2x+5 and 2x+5 to get \left(2x+5\right)^{2}.

$$\left(2x+5\right)^{2}-9\left(x+1\right)\left(x+1\right)$$

Multiply x+1 and x+1 to get \left(x+1\right)^{2}.

$$\left(2x+5\right)^{2}-9\left(x+1\right)^{2}$$

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

$$4x^{2}+20x+25-9\left(x+1\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+1\right)^{2}.

$$4x^{2}+20x+25-9\left(x^{2}+2x+1\right)$$

Use the distributive property to multiply -9 by x^{2}+2x+1.

$$4x^{2}+20x+25-9x^{2}-18x-9$$

Combine 4x^{2} and -9x^{2} to get -5x^{2}.

$$-5x^{2}+20x+25-18x-9$$

Combine 20x and -18x to get 2x.

$$-5x^{2}+2x+25-9$$

Subtract 9 from 25 to get 16.

$$-5x^{2}+2x+16$$

Expand

$$16+2x-5x^{2}$$

Solution Steps

Multiply 2x+5 and 2x+5 to get \left(2x+5\right)^{2}.

$$\left(2x+5\right)^{2}-9\left(x+1\right)\left(x+1\right)$$

Multiply x+1 and x+1 to get \left(x+1\right)^{2}.

$$\left(2x+5\right)^{2}-9\left(x+1\right)^{2}$$

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

$$4x^{2}+20x+25-9\left(x+1\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+1\right)^{2}.

$$4x^{2}+20x+25-9\left(x^{2}+2x+1\right)$$

Use the distributive property to multiply -9 by x^{2}+2x+1.

$$4x^{2}+20x+25-9x^{2}-18x-9$$

Combine 4x^{2} and -9x^{2} to get -5x^{2}.

$$-5x^{2}+20x+25-18x-9$$

Combine 20x and -18x to get 2x.

$$-5x^{2}+2x+25-9$$

Subtract 9 from 25 to get 16.

$$-5x^{2}+2x+16$$