Solve (73)x-{5+3[(x+1)(x-1)+6x]}

$$( 73 ) x - \{ 5 + 3 [ ( x + 1 ) ( x - 1 ) + 6 x ] \}$$

Evaluate

$$-3x^{2}+55x-2$$

Solution Steps

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}.

$$73x-\left(5+3\left(x^{2}-1^{2}+6x\right)\right)$$

Calculate 1 to the power of 2 and get 1.

$$73x-\left(5+3\left(x^{2}-1+6x\right)\right)$$

Use the distributive property to multiply 3 by x^{2}-1+6x.

$$73x-\left(5+3x^{2}-3+18x\right)$$

Subtract 3 from 5 to get 2.

$$73x-\left(2+3x^{2}+18x\right)$$

To find the opposite of 2+3x^{2}+18x, find the opposite of each term.

$$73x-2-3x^{2}-18x$$

Combine 73x and -18x to get 55x.

$$55x-2-3x^{2}$$

Expand

$$-3x^{2}+55x-2$$

Solution Steps

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}.

$$73x-\left(5+3\left(x^{2}-1^{2}+6x\right)\right)$$

Calculate 1 to the power of 2 and get 1.

$$73x-\left(5+3\left(x^{2}-1+6x\right)\right)$$

Use the distributive property to multiply 3 by x^{2}-1+6x.

$$73x-\left(5+3x^{2}-3+18x\right)$$

Subtract 3 from 5 to get 2.

$$73x-\left(2+3x^{2}+18x\right)$$

To find the opposite of 2+3x^{2}+18x, find the opposite of each term.

$$73x-2-3x^{2}-18x$$

Combine 73x and -18x to get 55x.

$$55x-2-3x^{2}$$