Solve -3(2x-1)+(x+1)(x-1)-5(x+2)

$$- 3 ( 2 x - 1 ) + ( x + 1 ) ( x - 1 ) - 5 ( x + 2 )$$

Evaluate

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

Solution Steps

Use the distributive property to multiply -3 by 2x-1.

$$-6x+3+\left(x+1\right)\left(x-1\right)-5\left(x+2\right)$$

Consider \left(x+1\right)\left(x-1\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$-6x+3+x^{2}-1^{2}-5\left(x+2\right)$$

Calculate 1 to the power of 2 and get 1.

$$-6x+3+x^{2}-1-5\left(x+2\right)$$

Subtract 1 from 3 to get 2.

$$-6x+2+x^{2}-5\left(x+2\right)$$

Use the distributive property to multiply -5 by x+2.

$$-6x+2+x^{2}-5x-10$$

Combine -6x and -5x to get -11x.

$$-11x+2+x^{2}-10$$

Subtract 10 from 2 to get -8.

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

Expand

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

Solution Steps

Use the distributive property to multiply -3 by 2x-1.

$$-6x+3+\left(x+1\right)\left(x-1\right)-5\left(x+2\right)$$

Consider \left(x+1\right)\left(x-1\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$-6x+3+x^{2}-1^{2}-5\left(x+2\right)$$

Calculate 1 to the power of 2 and get 1.

$$-6x+3+x^{2}-1-5\left(x+2\right)$$

Subtract 1 from 3 to get 2.

$$-6x+2+x^{2}-5\left(x+2\right)$$

Use the distributive property to multiply -5 by x+2.

$$-6x+2+x^{2}-5x-10$$

Combine -6x and -5x to get -11x.

$$-11x+2+x^{2}-10$$

Subtract 10 from 2 to get -8.

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