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

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

Evaluate

$$12b+6b^{2}+4a-17ab-7a^{2}$$

Solution Steps

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

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

Multiply a and a to get a^{2}.

$$a^{2}\left(-1\right)+3ab+2b\left(-1\right)a+6b^{2}-2\left(a+3b\right)\left(3a-2\right)$$

Multiply 2 and -1 to get -2.

$$a^{2}\left(-1\right)+3ab-2ba+6b^{2}-2\left(a+3b\right)\left(3a-2\right)$$

Combine 3ab and -2ba to get ab.

$$a^{2}\left(-1\right)+ab+6b^{2}-2\left(a+3b\right)\left(3a-2\right)$$

Use the distributive property to multiply -2 by a+3b.

$$a^{2}\left(-1\right)+ab+6b^{2}+\left(-2a-6b\right)\left(3a-2\right)$$

Apply the distributive property by multiplying each term of -2a-6b by each term of 3a-2.

$$a^{2}\left(-1\right)+ab+6b^{2}-6a^{2}+4a-18ba+12b$$

Combine a^{2}\left(-1\right) and -6a^{2} to get -7a^{2}.

$$-7a^{2}+ab+6b^{2}+4a-18ba+12b$$

Combine ab and -18ba to get -17ab.

$$-7a^{2}-17ab+6b^{2}+4a+12b$$

Expand

$$12b+6b^{2}+4a-17ab-7a^{2}$$

Solution Steps

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

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

Multiply a and a to get a^{2}.

$$a^{2}\left(-1\right)+3ab+2b\left(-1\right)a+6b^{2}-2\left(a+3b\right)\left(3a-2\right)$$

Multiply 2 and -1 to get -2.

$$a^{2}\left(-1\right)+3ab-2ba+6b^{2}-2\left(a+3b\right)\left(3a-2\right)$$

Combine 3ab and -2ba to get ab.

$$a^{2}\left(-1\right)+ab+6b^{2}-2\left(a+3b\right)\left(3a-2\right)$$

Use the distributive property to multiply -2 by a+3b.

$$a^{2}\left(-1\right)+ab+6b^{2}+\left(-2a-6b\right)\left(3a-2\right)$$

Apply the distributive property by multiplying each term of -2a-6b by each term of 3a-2.

$$a^{2}\left(-1\right)+ab+6b^{2}-6a^{2}+4a-18ba+12b$$

Combine a^{2}\left(-1\right) and -6a^{2} to get -7a^{2}.

$$-7a^{2}+ab+6b^{2}+4a-18ba+12b$$

Combine ab and -18ba to get -17ab.

$$-7a^{2}-17ab+6b^{2}+4a+12b$$