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

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

Evaluate

$$5x^{2}-34$$

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}.

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

Calculate 5 to the power of 2 and get 25.

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

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

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

Calculate 3 to the power of 2 and get 9.

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

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

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

Calculate 2 to the power of 2 and get 4.

$$x^{2}-25-\left(9-4x^{2}\right)$$

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

$$x^{2}-25-9-\left(-4x^{2}\right)$$

The opposite of -4x^{2} is 4x^{2}.

$$x^{2}-25-9+4x^{2}$$

Subtract 9 from -25 to get -34.

$$x^{2}-34+4x^{2}$$

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

$$5x^{2}-34$$

Expand

$$5x^{2}-34$$

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}.

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

Calculate 5 to the power of 2 and get 25.

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

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

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

Calculate 3 to the power of 2 and get 9.

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

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

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

Calculate 2 to the power of 2 and get 4.

$$x^{2}-25-\left(9-4x^{2}\right)$$

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

$$x^{2}-25-9-\left(-4x^{2}\right)$$

The opposite of -4x^{2} is 4x^{2}.

$$x^{2}-25-9+4x^{2}$$

Subtract 9 from -25 to get -34.

$$x^{2}-34+4x^{2}$$

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

$$5x^{2}-34$$