Solve 4(x-1)^2-(2x+3)(2x-3)

$$4 ( x - 1 ) ^ { 2 } - ( 2 x + 3 ) ( 2 x - 3 )$$

Evaluate

$$13-8x$$

Solution Steps

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

$$4\left(x^{2}-2x+1\right)-\left(2x+3\right)\left(2x-3\right)$$

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

$$4x^{2}-8x+4-\left(2x+3\right)\left(2x-3\right)$$

Consider \left(2x+3\right)\left(2x-3\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 3.

$$4x^{2}-8x+4-\left(\left(2x\right)^{2}-9\right)$$

Expand \left(2x\right)^{2}.

$$4x^{2}-8x+4-\left(2^{2}x^{2}-9\right)$$

Calculate 2 to the power of 2 and get 4.

$$4x^{2}-8x+4-\left(4x^{2}-9\right)$$

To find the opposite of 4x^{2}-9, find the opposite of each term.

$$4x^{2}-8x+4-4x^{2}+9$$

Combine 4x^{2} and -4x^{2} to get 0.

$$-8x+4+9$$

Add 4 and 9 to get 13.

$$-8x+13$$

Expand

$$13-8x$$

Solution Steps

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

$$4\left(x^{2}-2x+1\right)-\left(2x+3\right)\left(2x-3\right)$$

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

$$4x^{2}-8x+4-\left(2x+3\right)\left(2x-3\right)$$

Consider \left(2x+3\right)\left(2x-3\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 3.

$$4x^{2}-8x+4-\left(\left(2x\right)^{2}-9\right)$$

Expand \left(2x\right)^{2}.

$$4x^{2}-8x+4-\left(2^{2}x^{2}-9\right)$$

Calculate 2 to the power of 2 and get 4.

$$4x^{2}-8x+4-\left(4x^{2}-9\right)$$

To find the opposite of 4x^{2}-9, find the opposite of each term.

$$4x^{2}-8x+4-4x^{2}+9$$

Combine 4x^{2} and -4x^{2} to get 0.

$$-8x+4+9$$

Add 4 and 9 to get 13.

$$-8x+13$$