Solve 3*3(x-1)^2-(2x+3)(2x-3)

$$3 \cdot 3 ( x - 1 ) ^ { 2 } - ( 2 x + 3 ) ( 2 x - 3 )$$

Evaluate

$$5x^{2}-18x+18$$

Solution Steps

Multiply 3 and 3 to get 9.

$$9\left(x-1\right)^{2}-\left(2x+3\right)\left(2x-3\right)$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-1\right)^{2}.

$$9\left(x^{2}-2x+1\right)-\left(2x+3\right)\left(2x-3\right)$$

Use the distributive property to multiply 9 by x^{2}-2x+1.

$$9x^{2}-18x+9-\left(2x+3\right)\left(2x-3\right)$$

Consider \left(2x+3\right)\left(2x-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}. Square 3.

$$9x^{2}-18x+9-\left(\left(2x\right)^{2}-9\right)$$

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

$$9x^{2}-18x+9-\left(2^{2}x^{2}-9\right)$$

Calculate 2 to the power of 2 and get 4.

$$9x^{2}-18x+9-\left(4x^{2}-9\right)$$

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

$$9x^{2}-18x+9-4x^{2}+9$$

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

$$5x^{2}-18x+9+9$$

Add 9 and 9 to get 18.

$$5x^{2}-18x+18$$

Expand

$$5x^{2}-18x+18$$

Solution Steps

Multiply 3 and 3 to get 9.

$$9\left(x-1\right)^{2}-\left(2x+3\right)\left(2x-3\right)$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-1\right)^{2}.

$$9\left(x^{2}-2x+1\right)-\left(2x+3\right)\left(2x-3\right)$$

Use the distributive property to multiply 9 by x^{2}-2x+1.

$$9x^{2}-18x+9-\left(2x+3\right)\left(2x-3\right)$$

Consider \left(2x+3\right)\left(2x-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}. Square 3.

$$9x^{2}-18x+9-\left(\left(2x\right)^{2}-9\right)$$

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

$$9x^{2}-18x+9-\left(2^{2}x^{2}-9\right)$$

Calculate 2 to the power of 2 and get 4.

$$9x^{2}-18x+9-\left(4x^{2}-9\right)$$

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

$$9x^{2}-18x+9-4x^{2}+9$$

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

$$5x^{2}-18x+9+9$$

Add 9 and 9 to get 18.

$$5x^{2}-18x+18$$