Solve left(2x-5right)^2-left(x-6right)^2

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

Evaluate

$$\left(3x-11\right)\left(x+1\right)$$

Solution Steps

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

$$4x^{2}-20x+25-\left(x-6\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-6\right)^{2}.

$$4x^{2}-20x+25-\left(x^{2}-12x+36\right)$$

To find the opposite of x^{2}-12x+36, find the opposite of each term.

$$4x^{2}-20x+25-x^{2}+12x-36$$

Combine 4x^{2} and -x^{2} to get 3x^{2}.

$$3x^{2}-20x+25+12x-36$$

Combine -20x and 12x to get -8x.

$$3x^{2}-8x+25-36$$

Subtract 36 from 25 to get -11.

$$3x^{2}-8x-11$$

Expand

$$3x^{2}-8x-11$$

Solution Steps

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

$$4x^{2}-20x+25-\left(x-6\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-6\right)^{2}.

$$4x^{2}-20x+25-\left(x^{2}-12x+36\right)$$

To find the opposite of x^{2}-12x+36, find the opposite of each term.

$$4x^{2}-20x+25-x^{2}+12x-36$$

Combine 4x^{2} and -x^{2} to get 3x^{2}.

$$3x^{2}-20x+25+12x-36$$

Combine -20x and 12x to get -8x.

$$3x^{2}-8x+25-36$$

Subtract 36 from 25 to get -11.

$$3x^{2}-8x-11$$