Solve (d-5)(d-2)-(d-4)(d+4)

$$( d - 5 ) ( d - 2 ) - ( d - 4 ) ( d + 4 )$$

Evaluate

$$26-7d$$

Solution Steps

Apply the distributive property by multiplying each term of d-5 by each term of d-2.

$$d^{2}-2d-5d+10-\left(d-4\right)\left(d+4\right)$$

Combine -2d and -5d to get -7d.

$$d^{2}-7d+10-\left(d-4\right)\left(d+4\right)$$

Consider \left(d-4\right)\left(d+4\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$d^{2}-7d+10-\left(d^{2}-4^{2}\right)$$

Calculate 4 to the power of 2 and get 16.

$$d^{2}-7d+10-\left(d^{2}-16\right)$$

To find the opposite of d^{2}-16, find the opposite of each term.

$$d^{2}-7d+10-d^{2}-\left(-16\right)$$

The opposite of -16 is 16.

$$d^{2}-7d+10-d^{2}+16$$

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

$$-7d+10+16$$

Add 10 and 16 to get 26.

$$-7d+26$$

Expand

$$26-7d$$

Solution Steps

Apply the distributive property by multiplying each term of d-5 by each term of d-2.

$$d^{2}-2d-5d+10-\left(d-4\right)\left(d+4\right)$$

Combine -2d and -5d to get -7d.

$$d^{2}-7d+10-\left(d-4\right)\left(d+4\right)$$

Consider \left(d-4\right)\left(d+4\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$d^{2}-7d+10-\left(d^{2}-4^{2}\right)$$

Calculate 4 to the power of 2 and get 16.

$$d^{2}-7d+10-\left(d^{2}-16\right)$$

To find the opposite of d^{2}-16, find the opposite of each term.

$$d^{2}-7d+10-d^{2}-\left(-16\right)$$

The opposite of -16 is 16.

$$d^{2}-7d+10-d^{2}+16$$

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

$$-7d+10+16$$

Add 10 and 16 to get 26.

$$-7d+26$$