Solve left(2x-3right)^2-left(3x+6right)^2

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

Evaluate

$$-\left(x+9\right)\left(5x+3\right)$$

Solution Steps

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

$$4x^{2}-12x+9-\left(3x+6\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(3x+6\right)^{2}.

$$4x^{2}-12x+9-\left(9x^{2}+36x+36\right)$$

To find the opposite of 9x^{2}+36x+36, find the opposite of each term.

$$4x^{2}-12x+9-9x^{2}-36x-36$$

Combine 4x^{2} and -9x^{2} to get -5x^{2}.

$$-5x^{2}-12x+9-36x-36$$

Combine -12x and -36x to get -48x.

$$-5x^{2}-48x+9-36$$

Subtract 36 from 9 to get -27.

$$-5x^{2}-48x-27$$

Expand

$$-5x^{2}-48x-27$$

Solution Steps

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

$$4x^{2}-12x+9-\left(3x+6\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(3x+6\right)^{2}.

$$4x^{2}-12x+9-\left(9x^{2}+36x+36\right)$$

To find the opposite of 9x^{2}+36x+36, find the opposite of each term.

$$4x^{2}-12x+9-9x^{2}-36x-36$$

Combine 4x^{2} and -9x^{2} to get -5x^{2}.

$$-5x^{2}-12x+9-36x-36$$

Combine -12x and -36x to get -48x.

$$-5x^{2}-48x+9-36$$

Subtract 36 from 9 to get -27.

$$-5x^{2}-48x-27$$