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

$$( x + 2 ) ( x - 2 ) + ( 3 x - 4 ) ( 1 - 2 x )$$

Evaluate

$$-5x^{2}+11x-8$$

Solution Steps

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

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

Calculate 2 to the power of 2 and get 4.

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

Apply the distributive property by multiplying each term of 3x-4 by each term of 1-2x.

$$x^{2}-4+3x-6x^{2}-4+8x$$

Combine 3x and 8x to get 11x.

$$x^{2}-4+11x-6x^{2}-4$$

Combine x^{2} and -6x^{2} to get -5x^{2}.

$$-5x^{2}-4+11x-4$$

Subtract 4 from -4 to get -8.

$$-5x^{2}-8+11x$$

Expand

$$-5x^{2}+11x-8$$

Solution Steps

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

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

Calculate 2 to the power of 2 and get 4.

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

Apply the distributive property by multiplying each term of 3x-4 by each term of 1-2x.

$$x^{2}-4+3x-6x^{2}-4+8x$$

Combine 3x and 8x to get 11x.

$$x^{2}-4+11x-6x^{2}-4$$

Combine x^{2} and -6x^{2} to get -5x^{2}.

$$-5x^{2}-4+11x-4$$

Subtract 4 from -4 to get -8.

$$-5x^{2}-8+11x$$