Solve (w+9)(w-9)-(w-5)(w-9)

$$( w + 9 ) ( w - 9 ) - ( w - 5 ) ( w - 9 )$$

Evaluate

$$14\left(w-9\right)$$

Solution Steps

Consider \left(w+9\right)\left(w-9\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$w^{2}-9^{2}-\left(w-5\right)\left(w-9\right)$$

Calculate 9 to the power of 2 and get 81.

$$w^{2}-81-\left(w-5\right)\left(w-9\right)$$

Apply the distributive property by multiplying each term of w-5 by each term of w-9.

$$w^{2}-81-\left(w^{2}-9w-5w+45\right)$$

Combine -9w and -5w to get -14w.

$$w^{2}-81-\left(w^{2}-14w+45\right)$$

To find the opposite of w^{2}-14w+45, find the opposite of each term.

$$w^{2}-81-w^{2}-\left(-14w\right)-45$$

The opposite of -14w is 14w.

$$w^{2}-81-w^{2}+14w-45$$

Combine w^{2} and -w^{2} to get 0.

$$-81+14w-45$$

Subtract 45 from -81 to get -126.

$$-126+14w$$

Expand

$$14w-126$$

Solution Steps

Consider \left(w+9\right)\left(w-9\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$w^{2}-9^{2}-\left(w-5\right)\left(w-9\right)$$

Calculate 9 to the power of 2 and get 81.

$$w^{2}-81-\left(w-5\right)\left(w-9\right)$$

Apply the distributive property by multiplying each term of w-5 by each term of w-9.

$$w^{2}-81-\left(w^{2}-9w-5w+45\right)$$

Combine -9w and -5w to get -14w.

$$w^{2}-81-\left(w^{2}-14w+45\right)$$

To find the opposite of w^{2}-14w+45, find the opposite of each term.

$$w^{2}-81-w^{2}-\left(-14w\right)-45$$

The opposite of -14w is 14w.

$$w^{2}-81-w^{2}+14w-45$$

Combine w^{2} and -w^{2} to get 0.

$$-81+14w-45$$

Subtract 45 from -81 to get -126.

$$-126+14w$$