Solve (2x-7)(x-1)+(2x-3)(2x+3)

$$(2x-7)(x-1)+(2x-3)(2x+3)$$

Evaluate

$$6x^{2}-9x-2$$

Solution Steps

Apply the distributive property by multiplying each term of 2x-7 by each term of x-1.

$$2x^{2}-2x-7x+7+\left(2x-3\right)\left(2x+3\right)$$

Combine -2x and -7x to get -9x.

$$2x^{2}-9x+7+\left(2x-3\right)\left(2x+3\right)$$

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}.

$$2x^{2}-9x+7+\left(2x\right)^{2}-3^{2}$$

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

$$2x^{2}-9x+7+2^{2}x^{2}-3^{2}$$

Calculate 2 to the power of 2 and get 4.

$$2x^{2}-9x+7+4x^{2}-3^{2}$$

Calculate 3 to the power of 2 and get 9.

$$2x^{2}-9x+7+4x^{2}-9$$

Combine 2x^{2} and 4x^{2} to get 6x^{2}.

$$6x^{2}-9x+7-9$$

Subtract 9 from 7 to get -2.

$$6x^{2}-9x-2$$

Expand

$$6x^{2}-9x-2$$

Solution Steps

Apply the distributive property by multiplying each term of 2x-7 by each term of x-1.

$$2x^{2}-2x-7x+7+\left(2x-3\right)\left(2x+3\right)$$

Combine -2x and -7x to get -9x.

$$2x^{2}-9x+7+\left(2x-3\right)\left(2x+3\right)$$

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}.

$$2x^{2}-9x+7+\left(2x\right)^{2}-3^{2}$$

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

$$2x^{2}-9x+7+2^{2}x^{2}-3^{2}$$

Calculate 2 to the power of 2 and get 4.

$$2x^{2}-9x+7+4x^{2}-3^{2}$$

Calculate 3 to the power of 2 and get 9.

$$2x^{2}-9x+7+4x^{2}-9$$

Combine 2x^{2} and 4x^{2} to get 6x^{2}.

$$6x^{2}-9x+7-9$$

Subtract 9 from 7 to get -2.

$$6x^{2}-9x-2$$