Solve (3x-5)(5x-11)-(5-3x)^2+2(3x-5)(x+2)

$$( 3 x - 5 ) ( 5 x - 11 ) - ( 5 - 3 x ) ^ { 2 } + 2 ( 3 x - 5 ) ( x + 2 )$$

Evaluate

$$12x^{2}-26x+10$$

Solution Steps

Use the distributive property to multiply 3x-5 by 5x-11 and combine like terms.

$$15x^{2}-58x+55-\left(5-3x\right)^{2}+2\left(3x-5\right)\left(x+2\right)$$

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

$$15x^{2}-58x+55-\left(25-30x+9x^{2}\right)+2\left(3x-5\right)\left(x+2\right)$$

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

$$15x^{2}-58x+55-25+30x-9x^{2}+2\left(3x-5\right)\left(x+2\right)$$

Subtract 25 from 55 to get 30.

$$15x^{2}-58x+30+30x-9x^{2}+2\left(3x-5\right)\left(x+2\right)$$

Combine -58x and 30x to get -28x.

$$15x^{2}-28x+30-9x^{2}+2\left(3x-5\right)\left(x+2\right)$$

Combine 15x^{2} and -9x^{2} to get 6x^{2}.

$$6x^{2}-28x+30+2\left(3x-5\right)\left(x+2\right)$$

Use the distributive property to multiply 2 by 3x-5.

$$6x^{2}-28x+30+\left(6x-10\right)\left(x+2\right)$$

Use the distributive property to multiply 6x-10 by x+2 and combine like terms.

$$6x^{2}-28x+30+6x^{2}+2x-20$$

Combine 6x^{2} and 6x^{2} to get 12x^{2}.

$$12x^{2}-28x+30+2x-20$$

Combine -28x and 2x to get -26x.

$$12x^{2}-26x+30-20$$

Subtract 20 from 30 to get 10.

$$12x^{2}-26x+10$$

Expand

$$12x^{2}-26x+10$$

Solution Steps

Use the distributive property to multiply 3x-5 by 5x-11 and combine like terms.

$$15x^{2}-58x+55-\left(5-3x\right)^{2}+2\left(3x-5\right)\left(x+2\right)$$

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

$$15x^{2}-58x+55-\left(25-30x+9x^{2}\right)+2\left(3x-5\right)\left(x+2\right)$$

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

$$15x^{2}-58x+55-25+30x-9x^{2}+2\left(3x-5\right)\left(x+2\right)$$

Subtract 25 from 55 to get 30.

$$15x^{2}-58x+30+30x-9x^{2}+2\left(3x-5\right)\left(x+2\right)$$

Combine -58x and 30x to get -28x.

$$15x^{2}-28x+30-9x^{2}+2\left(3x-5\right)\left(x+2\right)$$

Combine 15x^{2} and -9x^{2} to get 6x^{2}.

$$6x^{2}-28x+30+2\left(3x-5\right)\left(x+2\right)$$

Use the distributive property to multiply 2 by 3x-5.

$$6x^{2}-28x+30+\left(6x-10\right)\left(x+2\right)$$

Use the distributive property to multiply 6x-10 by x+2 and combine like terms.

$$6x^{2}-28x+30+6x^{2}+2x-20$$

Combine 6x^{2} and 6x^{2} to get 12x^{2}.

$$12x^{2}-28x+30+2x-20$$

Combine -28x and 2x to get -26x.

$$12x^{2}-26x+30-20$$

Subtract 20 from 30 to get 10.

$$12x^{2}-26x+10$$