Solve (w+2)(w-2)+(4w+3)(w-2)

$$( w + 2 ) ( w - 2 ) + ( 4 w + 3 ) ( w - 2 )$$

Evaluate

$$5\left(w-2\right)\left(w+1\right)$$

Solution Steps

Consider \left(w+2\right)\left(w-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}.

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

Calculate 2 to the power of 2 and get 4.

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

Apply the distributive property by multiplying each term of 4w+3 by each term of w-2.

$$w^{2}-4+4w^{2}-8w+3w-6$$

Combine -8w and 3w to get -5w.

$$w^{2}-4+4w^{2}-5w-6$$

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

$$5w^{2}-4-5w-6$$

Subtract 6 from -4 to get -10.

$$5w^{2}-10-5w$$

Expand

$$5w^{2}-5w-10$$

Solution Steps

Consider \left(w+2\right)\left(w-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}.

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

Calculate 2 to the power of 2 and get 4.

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

Apply the distributive property by multiplying each term of 4w+3 by each term of w-2.

$$w^{2}-4+4w^{2}-8w+3w-6$$

Combine -8w and 3w to get -5w.

$$w^{2}-4+4w^{2}-5w-6$$

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

$$5w^{2}-4-5w-6$$

Subtract 6 from -4 to get -10.

$$5w^{2}-10-5w$$