Solve left(5left(a+bright)-2right)left(3left(a+bright)+5right)=

$$\left( 5 \left( a+b \right) -2 \right) \left( 3 \left( a+b \right) +5 \right) =$$

Evaluate

$$\left(5a+5b-2\right)\left(3a+3b+5\right)$$

Solution Steps

Use the distributive property to multiply 5 by a+b.

$$\left(5a+5b-2\right)\left(3\left(a+b\right)+5\right)$$

Use the distributive property to multiply 3 by a+b.

$$\left(5a+5b-2\right)\left(3a+3b+5\right)$$

Apply the distributive property by multiplying each term of 5a+5b-2 by each term of 3a+3b+5.

$$15a^{2}+15ab+25a+15ab+15b^{2}+25b-6a-6b-10$$

Combine 15ab and 15ab to get 30ab.

$$15a^{2}+30ab+25a+15b^{2}+25b-6a-6b-10$$

Combine 25a and -6a to get 19a.

$$15a^{2}+30ab+19a+15b^{2}+25b-6b-10$$

Combine 25b and -6b to get 19b.

$$15a^{2}+30ab+19a+15b^{2}+19b-10$$

Expand

$$15a^{2}+30ab+19a+15b^{2}+19b-10$$

Solution Steps

Use the distributive property to multiply 5 by a+b.

$$\left(5a+5b-2\right)\left(3\left(a+b\right)+5\right)$$

Use the distributive property to multiply 3 by a+b.

$$\left(5a+5b-2\right)\left(3a+3b+5\right)$$

Apply the distributive property by multiplying each term of 5a+5b-2 by each term of 3a+3b+5.

$$15a^{2}+15ab+25a+15ab+15b^{2}+25b-6a-6b-10$$

Combine 15ab and 15ab to get 30ab.

$$15a^{2}+30ab+25a+15b^{2}+25b-6a-6b-10$$

Combine 25a and -6a to get 19a.

$$15a^{2}+30ab+19a+15b^{2}+25b-6b-10$$

Combine 25b and -6b to get 19b.

$$15a^{2}+30ab+19a+15b^{2}+19b-10$$