Solve (a+2b)2-(a+2b)(3a-7b)

$$( a + 2 b ) 2 - ( a + 2 b ) ( 3 a - 7 b )$$

Evaluate

$$\left(a+2b\right)\left(2+7b-3a\right)$$

Solution Steps

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

$$2a+4b-\left(a+2b\right)\left(3a-7b\right)$$

Apply the distributive property by multiplying each term of a+2b by each term of 3a-7b.

$$2a+4b-\left(3a^{2}-7ab+6ba-14b^{2}\right)$$

Combine -7ab and 6ba to get -ab.

$$2a+4b-\left(3a^{2}-ab-14b^{2}\right)$$

To find the opposite of 3a^{2}-ab-14b^{2}, find the opposite of each term.

$$2a+4b-3a^{2}-\left(-ab\right)-\left(-14b^{2}\right)$$

The opposite of -ab is ab.

$$2a+4b-3a^{2}+ab-\left(-14b^{2}\right)$$

The opposite of -14b^{2} is 14b^{2}.

$$2a+4b-3a^{2}+ab+14b^{2}$$

Expand

$$4b+14b^{2}+2a+ab-3a^{2}$$

Solution Steps

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

$$2a+4b-\left(a+2b\right)\left(3a-7b\right)$$

Apply the distributive property by multiplying each term of a+2b by each term of 3a-7b.

$$2a+4b-\left(3a^{2}-7ab+6ba-14b^{2}\right)$$

Combine -7ab and 6ba to get -ab.

$$2a+4b-\left(3a^{2}-ab-14b^{2}\right)$$

To find the opposite of 3a^{2}-ab-14b^{2}, find the opposite of each term.

$$2a+4b-3a^{2}-\left(-ab\right)-\left(-14b^{2}\right)$$

The opposite of -ab is ab.

$$2a+4b-3a^{2}+ab-\left(-14b^{2}\right)$$

The opposite of -14b^{2} is 14b^{2}.

$$2a+4b-3a^{2}+ab+14b^{2}$$