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

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

Evaluate

$$\left(x-9\right)\left(x-1\right)$$

Solution Steps

Use the distributive property to multiply 5x by x-2.

$$5x^{2}-10x-\left(2x+3\right)\left(2x-3\right)$$

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}.

$$5x^{2}-10x-\left(\left(2x\right)^{2}-3^{2}\right)$$

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

$$5x^{2}-10x-\left(2^{2}x^{2}-3^{2}\right)$$

Calculate 2 to the power of 2 and get 4.

$$5x^{2}-10x-\left(4x^{2}-3^{2}\right)$$

Calculate 3 to the power of 2 and get 9.

$$5x^{2}-10x-\left(4x^{2}-9\right)$$

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

$$5x^{2}-10x-4x^{2}-\left(-9\right)$$

The opposite of -9 is 9.

$$5x^{2}-10x-4x^{2}+9$$

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

$$x^{2}-10x+9$$

Expand

$$x^{2}-10x+9$$

Solution Steps

Use the distributive property to multiply 5x by x-2.

$$5x^{2}-10x-\left(2x+3\right)\left(2x-3\right)$$

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}.

$$5x^{2}-10x-\left(\left(2x\right)^{2}-3^{2}\right)$$

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

$$5x^{2}-10x-\left(2^{2}x^{2}-3^{2}\right)$$

Calculate 2 to the power of 2 and get 4.

$$5x^{2}-10x-\left(4x^{2}-3^{2}\right)$$

Calculate 3 to the power of 2 and get 9.

$$5x^{2}-10x-\left(4x^{2}-9\right)$$

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

$$5x^{2}-10x-4x^{2}-\left(-9\right)$$

The opposite of -9 is 9.

$$5x^{2}-10x-4x^{2}+9$$

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

$$x^{2}-10x+9$$