Solve 16(2x+1)^2-9(x-2)^2

$$16 ( 2 x + 1 ) ^ { 2 } - 9 ( x - 2 ) ^ { 2 }$$

Evaluate

$$5\left(11x-2\right)\left(x+2\right)$$

Solution Steps

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

$$16\left(4x^{2}+4x+1\right)-9\left(x-2\right)^{2}$$

Use the distributive property to multiply 16 by 4x^{2}+4x+1.

$$64x^{2}+64x+16-9\left(x-2\right)^{2}$$

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

$$64x^{2}+64x+16-9\left(x^{2}-4x+4\right)$$

Use the distributive property to multiply -9 by x^{2}-4x+4.

$$64x^{2}+64x+16-9x^{2}+36x-36$$

Combine 64x^{2} and -9x^{2} to get 55x^{2}.

$$55x^{2}+64x+16+36x-36$$

Combine 64x and 36x to get 100x.

$$55x^{2}+100x+16-36$$

Subtract 36 from 16 to get -20.

$$55x^{2}+100x-20$$

Expand

$$55x^{2}+100x-20$$

Solution Steps

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

$$16\left(4x^{2}+4x+1\right)-9\left(x-2\right)^{2}$$

Use the distributive property to multiply 16 by 4x^{2}+4x+1.

$$64x^{2}+64x+16-9\left(x-2\right)^{2}$$

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

$$64x^{2}+64x+16-9\left(x^{2}-4x+4\right)$$

Use the distributive property to multiply -9 by x^{2}-4x+4.

$$64x^{2}+64x+16-9x^{2}+36x-36$$

Combine 64x^{2} and -9x^{2} to get 55x^{2}.

$$55x^{2}+64x+16+36x-36$$

Combine 64x and 36x to get 100x.

$$55x^{2}+100x+16-36$$

Subtract 36 from 16 to get -20.

$$55x^{2}+100x-20$$