Solve left(x-5right)left(x+5right)-left(3x-4right)^2

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

Evaluate

$$-8x^{2}+24x-41$$

Solution Steps

Consider \left(x-5\right)\left(x+5\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 5.

$$x^{2}-25-\left(3x-4\right)^{2}$$

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

$$x^{2}-25-\left(9x^{2}-24x+16\right)$$

To find the opposite of 9x^{2}-24x+16, find the opposite of each term.

$$x^{2}-25-9x^{2}+24x-16$$

Combine x^{2} and -9x^{2} to get -8x^{2}.

$$-8x^{2}-25+24x-16$$

Subtract 16 from -25 to get -41.

$$-8x^{2}-41+24x$$

Expand

$$-8x^{2}+24x-41$$

Solution Steps

Consider \left(x-5\right)\left(x+5\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 5.

$$x^{2}-25-\left(3x-4\right)^{2}$$

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

$$x^{2}-25-\left(9x^{2}-24x+16\right)$$

To find the opposite of 9x^{2}-24x+16, find the opposite of each term.

$$x^{2}-25-9x^{2}+24x-16$$

Combine x^{2} and -9x^{2} to get -8x^{2}.

$$-8x^{2}-25+24x-16$$

Subtract 16 from -25 to get -41.

$$-8x^{2}-41+24x$$