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

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

Evaluate

$$6a^{2}+5ab-24b^{2}$$

Solution Steps

Use the distributive property to multiply 4 by 2a-3b.

$$\left(8a-12b\right)\left(a+2b\right)-a\left(2a-b\right)$$

Apply the distributive property by multiplying each term of 8a-12b by each term of a+2b.

$$8a^{2}+16ab-12ba-24b^{2}-a\left(2a-b\right)$$

Combine 16ab and -12ba to get 4ab.

$$8a^{2}+4ab-24b^{2}-a\left(2a-b\right)$$

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

$$8a^{2}+4ab-24b^{2}-\left(2a^{2}-ab\right)$$

To find the opposite of 2a^{2}-ab, find the opposite of each term.

$$8a^{2}+4ab-24b^{2}-2a^{2}-\left(-ab\right)$$

The opposite of -ab is ab.

$$8a^{2}+4ab-24b^{2}-2a^{2}+ab$$

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

$$6a^{2}+4ab-24b^{2}+ab$$

Combine 4ab and ab to get 5ab.

$$6a^{2}+5ab-24b^{2}$$

Expand

$$6a^{2}+5ab-24b^{2}$$

Solution Steps

Use the distributive property to multiply 4 by 2a-3b.

$$\left(8a-12b\right)\left(a+2b\right)-a\left(2a-b\right)$$

Apply the distributive property by multiplying each term of 8a-12b by each term of a+2b.

$$8a^{2}+16ab-12ba-24b^{2}-a\left(2a-b\right)$$

Combine 16ab and -12ba to get 4ab.

$$8a^{2}+4ab-24b^{2}-a\left(2a-b\right)$$

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

$$8a^{2}+4ab-24b^{2}-\left(2a^{2}-ab\right)$$

To find the opposite of 2a^{2}-ab, find the opposite of each term.

$$8a^{2}+4ab-24b^{2}-2a^{2}-\left(-ab\right)$$

The opposite of -ab is ab.

$$8a^{2}+4ab-24b^{2}-2a^{2}+ab$$

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

$$6a^{2}+4ab-24b^{2}+ab$$

Combine 4ab and ab to get 5ab.

$$6a^{2}+5ab-24b^{2}$$