Solve (x+3)(x-3)+(5x-6)(3x-7)

$$( x + 3 ) ( x - 3 ) + ( 5 x - 6 ) ( 3 x - 7 )$$

Evaluate

$$16x^{2}-53x+33$$

Solution Steps

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

$$x^{2}-3^{2}+\left(5x-6\right)\left(3x-7\right)$$

Calculate 3 to the power of 2 and get 9.

$$x^{2}-9+\left(5x-6\right)\left(3x-7\right)$$

Apply the distributive property by multiplying each term of 5x-6 by each term of 3x-7.

$$x^{2}-9+15x^{2}-35x-18x+42$$

Combine -35x and -18x to get -53x.

$$x^{2}-9+15x^{2}-53x+42$$

Combine x^{2} and 15x^{2} to get 16x^{2}.

$$16x^{2}-9-53x+42$$

Add -9 and 42 to get 33.

$$16x^{2}+33-53x$$

Expand

$$16x^{2}-53x+33$$

Solution Steps

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

$$x^{2}-3^{2}+\left(5x-6\right)\left(3x-7\right)$$

Calculate 3 to the power of 2 and get 9.

$$x^{2}-9+\left(5x-6\right)\left(3x-7\right)$$

Apply the distributive property by multiplying each term of 5x-6 by each term of 3x-7.

$$x^{2}-9+15x^{2}-35x-18x+42$$

Combine -35x and -18x to get -53x.

$$x^{2}-9+15x^{2}-53x+42$$

Combine x^{2} and 15x^{2} to get 16x^{2}.

$$16x^{2}-9-53x+42$$

Add -9 and 42 to get 33.

$$16x^{2}+33-53x$$