Solve (3a-2b)(a-b)+2(a-b)(a-2b)

$$( 3 a - 2 b ) ( a - b ) + 2 ( a - b ) ( a - 2 b )$$

Evaluate

$$\left(a-b\right)\left(5a-6b\right)$$

Solution Steps

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

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

Combine -3ab and -2ba to get -5ab.

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

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

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

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

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

Combine -4ab and -2ba to get -6ab.

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

Combine 3a^{2} and 2a^{2} to get 5a^{2}.

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

Combine -5ab and -6ab to get -11ab.

$$5a^{2}-11ab+2b^{2}+4b^{2}$$

Combine 2b^{2} and 4b^{2} to get 6b^{2}.

$$5a^{2}-11ab+6b^{2}$$

Expand

$$5a^{2}-11ab+6b^{2}$$

Solution Steps

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

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

Combine -3ab and -2ba to get -5ab.

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

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

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

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

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

Combine -4ab and -2ba to get -6ab.

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

Combine 3a^{2} and 2a^{2} to get 5a^{2}.

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

Combine -5ab and -6ab to get -11ab.

$$5a^{2}-11ab+2b^{2}+4b^{2}$$

Combine 2b^{2} and 4b^{2} to get 6b^{2}.

$$5a^{2}-11ab+6b^{2}$$