Solve (3-2x)^2+(2+3x)(2-3x)+5x^2-13

$$( 3 - 2 x ) ^ { 2 } + ( 2 + 3 x ) ( 2 - 3 x ) + 5 x ^ { 2 } - 13$$

Evaluate

$$-12x$$

Solution Steps

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

$$9-12x+4x^{2}+\left(2+3x\right)\left(2-3x\right)+5x^{2}-13$$

Consider \left(2+3x\right)\left(2-3x\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 2.

$$9-12x+4x^{2}+4-\left(3x\right)^{2}+5x^{2}-13$$

Expand \left(3x\right)^{2}.

$$9-12x+4x^{2}+4-3^{2}x^{2}+5x^{2}-13$$

Calculate 3 to the power of 2 and get 9.

$$9-12x+4x^{2}+4-9x^{2}+5x^{2}-13$$

Add 9 and 4 to get 13.

$$13-12x+4x^{2}-9x^{2}+5x^{2}-13$$

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

$$13-12x-5x^{2}+5x^{2}-13$$

Combine -5x^{2} and 5x^{2} to get 0.

$$13-12x-13$$

Subtract 13 from 13 to get 0.

$$-12x$$

Expand

$$-12x$$

Solution Steps

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

$$9-12x+4x^{2}+\left(2+3x\right)\left(2-3x\right)+5x^{2}-13$$

Consider \left(2+3x\right)\left(2-3x\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 2.

$$9-12x+4x^{2}+4-\left(3x\right)^{2}+5x^{2}-13$$

Expand \left(3x\right)^{2}.

$$9-12x+4x^{2}+4-3^{2}x^{2}+5x^{2}-13$$

Calculate 3 to the power of 2 and get 9.

$$9-12x+4x^{2}+4-9x^{2}+5x^{2}-13$$

Add 9 and 4 to get 13.

$$13-12x+4x^{2}-9x^{2}+5x^{2}-13$$

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

$$13-12x-5x^{2}+5x^{2}-13$$

Combine -5x^{2} and 5x^{2} to get 0.

$$13-12x-13$$

Subtract 13 from 13 to get 0.

$$-12x$$