Solve (5x+9)^2-4(x+1)^2

$$( 5 x + 9 ) ^ { 2 } - 4 ( x + 1 ) ^ { 2 }$$

Evaluate

$$\left(3x+7\right)\left(7x+11\right)$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(5x+9\right)^{2}.

$$25x^{2}+90x+81-4\left(x+1\right)^{2}$$

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

$$25x^{2}+90x+81-4\left(x^{2}+2x+1\right)$$

Use the distributive property to multiply -4 by x^{2}+2x+1.

$$25x^{2}+90x+81-4x^{2}-8x-4$$

Combine 25x^{2} and -4x^{2} to get 21x^{2}.

$$21x^{2}+90x+81-8x-4$$

Combine 90x and -8x to get 82x.

$$21x^{2}+82x+81-4$$

Subtract 4 from 81 to get 77.

$$21x^{2}+82x+77$$

Expand

$$21x^{2}+82x+77$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(5x+9\right)^{2}.

$$25x^{2}+90x+81-4\left(x+1\right)^{2}$$

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

$$25x^{2}+90x+81-4\left(x^{2}+2x+1\right)$$

Use the distributive property to multiply -4 by x^{2}+2x+1.

$$25x^{2}+90x+81-4x^{2}-8x-4$$

Combine 25x^{2} and -4x^{2} to get 21x^{2}.

$$21x^{2}+90x+81-8x-4$$

Combine 90x and -8x to get 82x.

$$21x^{2}+82x+81-4$$

Subtract 4 from 81 to get 77.

$$21x^{2}+82x+77$$