Solve 14x-(3x+5)^2-(10-x)(2x+8)

$$14 x - ( 3 x + 5 ) ^ { 2 } - ( 10 - x ) ( 2 x + 8 )$$

Evaluate

$$-7x^{2}-28x-105$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(3x+5\right)^{2}.

$$14x-\left(9x^{2}+30x+25\right)-\left(10-x\right)\left(2x+8\right)$$

To find the opposite of 9x^{2}+30x+25, find the opposite of each term.

$$14x-9x^{2}-30x-25-\left(10-x\right)\left(2x+8\right)$$

Combine 14x and -30x to get -16x.

$$-16x-9x^{2}-25-\left(10-x\right)\left(2x+8\right)$$

Use the distributive property to multiply 10-x by 2x+8 and combine like terms.

$$-16x-9x^{2}-25-\left(12x+80-2x^{2}\right)$$

To find the opposite of 12x+80-2x^{2}, find the opposite of each term.

$$-16x-9x^{2}-25-12x-80+2x^{2}$$

Combine -16x and -12x to get -28x.

$$-28x-9x^{2}-25-80+2x^{2}$$

Subtract 80 from -25 to get -105.

$$-28x-9x^{2}-105+2x^{2}$$

Combine -9x^{2} and 2x^{2} to get -7x^{2}.

$$-28x-7x^{2}-105$$

Expand

$$-7x^{2}-28x-105$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(3x+5\right)^{2}.

$$14x-\left(9x^{2}+30x+25\right)-\left(10-x\right)\left(2x+8\right)$$

To find the opposite of 9x^{2}+30x+25, find the opposite of each term.

$$14x-9x^{2}-30x-25-\left(10-x\right)\left(2x+8\right)$$

Combine 14x and -30x to get -16x.

$$-16x-9x^{2}-25-\left(10-x\right)\left(2x+8\right)$$

Use the distributive property to multiply 10-x by 2x+8 and combine like terms.

$$-16x-9x^{2}-25-\left(12x+80-2x^{2}\right)$$

To find the opposite of 12x+80-2x^{2}, find the opposite of each term.

$$-16x-9x^{2}-25-12x-80+2x^{2}$$

Combine -16x and -12x to get -28x.

$$-28x-9x^{2}-25-80+2x^{2}$$

Subtract 80 from -25 to get -105.

$$-28x-9x^{2}-105+2x^{2}$$

Combine -9x^{2} and 2x^{2} to get -7x^{2}.

$$-28x-7x^{2}-105$$