Solve (2-3x)(3-5x)-left(2-3xright)^2

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

Evaluate

$$\left(1-2x\right)\left(2-3x\right)$$

Solution Steps

Use the distributive property to multiply 2-3x by 3-5x and combine like terms.

$$6-19x+15x^{2}-\left(2-3x\right)^{2}$$

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

$$6-19x+15x^{2}-\left(4-12x+9x^{2}\right)$$

To find the opposite of 4-12x+9x^{2}, find the opposite of each term.

$$6-19x+15x^{2}-4+12x-9x^{2}$$

Subtract 4 from 6 to get 2.

$$2-19x+15x^{2}+12x-9x^{2}$$

Combine -19x and 12x to get -7x.

$$2-7x+15x^{2}-9x^{2}$$

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

$$2-7x+6x^{2}$$

Expand

$$6x^{2}-7x+2$$

Solution Steps

Use the distributive property to multiply 2-3x by 3-5x and combine like terms.

$$6-19x+15x^{2}-\left(2-3x\right)^{2}$$

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

$$6-19x+15x^{2}-\left(4-12x+9x^{2}\right)$$

To find the opposite of 4-12x+9x^{2}, find the opposite of each term.

$$6-19x+15x^{2}-4+12x-9x^{2}$$

Subtract 4 from 6 to get 2.

$$2-19x+15x^{2}+12x-9x^{2}$$

Combine -19x and 12x to get -7x.

$$2-7x+15x^{2}-9x^{2}$$

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

$$2-7x+6x^{2}$$