Solve (4x-1)^2+2(4x-1)-14

$$( 4 x - 1 ) ^ { 2 } + 2 ( 4 x - 1 ) - 14$$

Evaluate

$$16x^{2}-15$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(4x-1\right)^{2}.

$$16x^{2}-8x+1+2\left(4x-1\right)-14$$

Use the distributive property to multiply 2 by 4x-1.

$$16x^{2}-8x+1+8x-2-14$$

Combine -8x and 8x to get 0.

$$16x^{2}+1-2-14$$

Subtract 2 from 1 to get -1.

$$16x^{2}-1-14$$

Subtract 14 from -1 to get -15.

$$16x^{2}-15$$

Expand

$$16x^{2}-15$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(4x-1\right)^{2}.

$$16x^{2}-8x+1+2\left(4x-1\right)-14$$

Use the distributive property to multiply 2 by 4x-1.

$$16x^{2}-8x+1+8x-2-14$$

Combine -8x and 8x to get 0.

$$16x^{2}+1-2-14$$

Subtract 2 from 1 to get -1.

$$16x^{2}-1-14$$

Subtract 14 from -1 to get -15.

$$16x^{2}-15$$