Solve (3x-4)(3x-4)-(3x-4)(2-5x)

$$( 3 x - 4 ) ( 3 x - 4 ) - ( 3 x - 4 ) ( 2 - 5 x )$$

Evaluate

$$24x^{2}-50x+24$$

Solution Steps

Multiply 3x-4 and 3x-4 to get \left(3x-4\right)^{2}.

$$\left(3x-4\right)^{2}-\left(3x-4\right)\left(2-5x\right)$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(3x-4\right)^{2}.

$$9x^{2}-24x+16-\left(3x-4\right)\left(2-5x\right)$$

Apply the distributive property by multiplying each term of 3x-4 by each term of 2-5x.

$$9x^{2}-24x+16-\left(6x-15x^{2}-8+20x\right)$$

Combine 6x and 20x to get 26x.

$$9x^{2}-24x+16-\left(26x-15x^{2}-8\right)$$

To find the opposite of 26x-15x^{2}-8, find the opposite of each term.

$$9x^{2}-24x+16-26x-\left(-15x^{2}\right)-\left(-8\right)$$

The opposite of -15x^{2} is 15x^{2}.

$$9x^{2}-24x+16-26x+15x^{2}-\left(-8\right)$$

The opposite of -8 is 8.

$$9x^{2}-24x+16-26x+15x^{2}+8$$

Combine -24x and -26x to get -50x.

$$9x^{2}-50x+16+15x^{2}+8$$

Combine 9x^{2} and 15x^{2} to get 24x^{2}.

$$24x^{2}-50x+16+8$$

Add 16 and 8 to get 24.

$$24x^{2}-50x+24$$

Expand

$$24x^{2}-50x+24$$

Solution Steps

Multiply 3x-4 and 3x-4 to get \left(3x-4\right)^{2}.

$$\left(3x-4\right)^{2}-\left(3x-4\right)\left(2-5x\right)$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(3x-4\right)^{2}.

$$9x^{2}-24x+16-\left(3x-4\right)\left(2-5x\right)$$

Apply the distributive property by multiplying each term of 3x-4 by each term of 2-5x.

$$9x^{2}-24x+16-\left(6x-15x^{2}-8+20x\right)$$

Combine 6x and 20x to get 26x.

$$9x^{2}-24x+16-\left(26x-15x^{2}-8\right)$$

To find the opposite of 26x-15x^{2}-8, find the opposite of each term.

$$9x^{2}-24x+16-26x-\left(-15x^{2}\right)-\left(-8\right)$$

The opposite of -15x^{2} is 15x^{2}.

$$9x^{2}-24x+16-26x+15x^{2}-\left(-8\right)$$

The opposite of -8 is 8.

$$9x^{2}-24x+16-26x+15x^{2}+8$$

Combine -24x and -26x to get -50x.

$$9x^{2}-50x+16+15x^{2}+8$$

Combine 9x^{2} and 15x^{2} to get 24x^{2}.

$$24x^{2}-50x+16+8$$

Add 16 and 8 to get 24.

$$24x^{2}-50x+24$$