Solve left(2a-bright)left(a+3bright)-2left(2a+bright)left(a-2bright)

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

Evaluate

$$b^{2}+11ab-2a^{2}$$

Solution Steps

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

$$2a^{2}+6ab-ba-3b^{2}-2\left(2a+b\right)\left(a-2b\right)$$

Combine 6ab and -ba to get 5ab.

$$2a^{2}+5ab-3b^{2}-2\left(2a+b\right)\left(a-2b\right)$$

Use the distributive property to multiply -2 by 2a+b.

$$2a^{2}+5ab-3b^{2}+\left(-4a-2b\right)\left(a-2b\right)$$

Apply the distributive property by multiplying each term of -4a-2b by each term of a-2b.

$$2a^{2}+5ab-3b^{2}-4a^{2}+8ab-2ba+4b^{2}$$

Combine 8ab and -2ba to get 6ab.

$$2a^{2}+5ab-3b^{2}-4a^{2}+6ab+4b^{2}$$

Combine 2a^{2} and -4a^{2} to get -2a^{2}.

$$-2a^{2}+5ab-3b^{2}+6ab+4b^{2}$$

Combine 5ab and 6ab to get 11ab.

$$-2a^{2}+11ab-3b^{2}+4b^{2}$$

Combine -3b^{2} and 4b^{2} to get b^{2}.

$$-2a^{2}+11ab+b^{2}$$

Expand

$$b^{2}+11ab-2a^{2}$$

Solution Steps

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

$$2a^{2}+6ab-ba-3b^{2}-2\left(2a+b\right)\left(a-2b\right)$$

Combine 6ab and -ba to get 5ab.

$$2a^{2}+5ab-3b^{2}-2\left(2a+b\right)\left(a-2b\right)$$

Use the distributive property to multiply -2 by 2a+b.

$$2a^{2}+5ab-3b^{2}+\left(-4a-2b\right)\left(a-2b\right)$$

Apply the distributive property by multiplying each term of -4a-2b by each term of a-2b.

$$2a^{2}+5ab-3b^{2}-4a^{2}+8ab-2ba+4b^{2}$$

Combine 8ab and -2ba to get 6ab.

$$2a^{2}+5ab-3b^{2}-4a^{2}+6ab+4b^{2}$$

Combine 2a^{2} and -4a^{2} to get -2a^{2}.

$$-2a^{2}+5ab-3b^{2}+6ab+4b^{2}$$

Combine 5ab and 6ab to get 11ab.

$$-2a^{2}+11ab-3b^{2}+4b^{2}$$

Combine -3b^{2} and 4b^{2} to get b^{2}.

$$-2a^{2}+11ab+b^{2}$$