Solve (a-2)*(a+2)-b(b+4)

$$( a - 2 ) \cdot ( a + 2 ) - b ( b + 4 )$$

Evaluate

$$-\left(-b-2\right)^{2}+a^{2}$$

Solution Steps

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

$$a^{2}-2^{2}-b\left(b+4\right)$$

Calculate 2 to the power of 2 and get 4.

$$a^{2}-4-b\left(b+4\right)$$

Use the distributive property to multiply b by b+4.

$$a^{2}-4-\left(b^{2}+4b\right)$$

To find the opposite of b^{2}+4b, find the opposite of each term.

$$a^{2}-4-b^{2}-4b$$

Expand

$$a^{2}-b^{2}-4b-4$$

Solution Steps

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

$$a^{2}-2^{2}-b\left(b+4\right)$$

Calculate 2 to the power of 2 and get 4.

$$a^{2}-4-b\left(b+4\right)$$

Use the distributive property to multiply b by b+4.

$$a^{2}-4-\left(b^{2}+4b\right)$$

To find the opposite of b^{2}+4b, find the opposite of each term.

$$a^{2}-4-b^{2}-4b$$