Solve -a(a-3b)-3(3a-b)(a-b)

$$- a ( a - 3 b ) - 3 ( 3 a - b ) ( a - b )$$

Evaluate

$$-10a^{2}+15ab-3b^{2}$$

Solution Steps

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

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

Multiply -3 and -1 to get 3.

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

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

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

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

$$-a^{2}+3ab+\left(-9a+3b\right)\left(a-b\right)$$

Apply the distributive property by multiplying each term of -9a+3b by each term of a-b.

$$-a^{2}+3ab-9a^{2}+9ab+3ba-3b^{2}$$

Combine 9ab and 3ba to get 12ab.

$$-a^{2}+3ab-9a^{2}+12ab-3b^{2}$$

Combine -a^{2} and -9a^{2} to get -10a^{2}.

$$-10a^{2}+3ab+12ab-3b^{2}$$

Combine 3ab and 12ab to get 15ab.

$$-10a^{2}+15ab-3b^{2}$$

Expand

$$-10a^{2}+15ab-3b^{2}$$

Solution Steps

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

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

Multiply -3 and -1 to get 3.

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

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

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

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

$$-a^{2}+3ab+\left(-9a+3b\right)\left(a-b\right)$$

Apply the distributive property by multiplying each term of -9a+3b by each term of a-b.

$$-a^{2}+3ab-9a^{2}+9ab+3ba-3b^{2}$$

Combine 9ab and 3ba to get 12ab.

$$-a^{2}+3ab-9a^{2}+12ab-3b^{2}$$

Combine -a^{2} and -9a^{2} to get -10a^{2}.

$$-10a^{2}+3ab+12ab-3b^{2}$$

Combine 3ab and 12ab to get 15ab.

$$-10a^{2}+15ab-3b^{2}$$