Solve 4a(3a-5b)-3a(2a+3b)+2a(a-2b)

$$4 a ( 3 a - 5 b ) - 3 a ( 2 a + 3 b ) + 2 a ( a - 2 b )$$

Evaluate

$$a\left(8a-33b\right)$$

Solution Steps

Use the distributive property to multiply 4a by 3a-5b.

$$12a^{2}-20ab-3a\left(2a+3b\right)+2a\left(a-2b\right)$$

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

$$12a^{2}-20ab-3a\left(2a+3b\right)+2a^{2}-4ab$$

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

$$12a^{2}-20ab-6a^{2}-9ab+2a^{2}-4ab$$

Combine 12a^{2} and -6a^{2} to get 6a^{2}.

$$6a^{2}-20ab-9ab+2a^{2}-4ab$$

Combine -20ab and -9ab to get -29ab.

$$6a^{2}-29ab+2a^{2}-4ab$$

Combine 6a^{2} and 2a^{2} to get 8a^{2}.

$$8a^{2}-29ab-4ab$$

Combine -29ab and -4ab to get -33ab.

$$8a^{2}-33ab$$

Expand

$$8a^{2}-33ab$$

Solution Steps

Use the distributive property to multiply 4a by 3a-5b.

$$12a^{2}-20ab-3a\left(2a+3b\right)+2a\left(a-2b\right)$$

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

$$12a^{2}-20ab-3a\left(2a+3b\right)+2a^{2}-4ab$$

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

$$12a^{2}-20ab-6a^{2}-9ab+2a^{2}-4ab$$

Combine 12a^{2} and -6a^{2} to get 6a^{2}.

$$6a^{2}-20ab-9ab+2a^{2}-4ab$$

Combine -20ab and -9ab to get -29ab.

$$6a^{2}-29ab+2a^{2}-4ab$$

Combine 6a^{2} and 2a^{2} to get 8a^{2}.

$$8a^{2}-29ab-4ab$$

Combine -29ab and -4ab to get -33ab.

$$8a^{2}-33ab$$