Solve (6a+b)(6a-b)-(9a-2b)(4a+3b)]:(-3b)

$$( 6 a + b ) ( 6 a - b ) - ( 9 a - 2 b ) ( 4 a + 3 b ) ] : ( - 3 b )$$

Evaluate

$$b\left(5b-19a\right)$$

Solution Steps

Consider \left(6a+b\right)\left(6a-b\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\left(6a\right)^{2}-b^{2}-\left(9a-2b\right)\left(4a+3b\right)$$

Expand \left(6a\right)^{2}.

$$6^{2}a^{2}-b^{2}-\left(9a-2b\right)\left(4a+3b\right)$$

Calculate 6 to the power of 2 and get 36.

$$36a^{2}-b^{2}-\left(9a-2b\right)\left(4a+3b\right)$$

Apply the distributive property by multiplying each term of 9a-2b by each term of 4a+3b.

$$36a^{2}-b^{2}-\left(36a^{2}+27ab-8ba-6b^{2}\right)$$

Combine 27ab and -8ba to get 19ab.

$$36a^{2}-b^{2}-\left(36a^{2}+19ab-6b^{2}\right)$$

To find the opposite of 36a^{2}+19ab-6b^{2}, find the opposite of each term.

$$36a^{2}-b^{2}-36a^{2}-19ab-\left(-6b^{2}\right)$$

The opposite of -6b^{2} is 6b^{2}.

$$36a^{2}-b^{2}-36a^{2}-19ab+6b^{2}$$

Combine 36a^{2} and -36a^{2} to get 0.

$$-b^{2}-19ab+6b^{2}$$

Combine -b^{2} and 6b^{2} to get 5b^{2}.

$$5b^{2}-19ab$$

Expand

$$5b^{2}-19ab$$

Solution Steps

Consider \left(6a+b\right)\left(6a-b\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\left(6a\right)^{2}-b^{2}-\left(9a-2b\right)\left(4a+3b\right)$$

Expand \left(6a\right)^{2}.

$$6^{2}a^{2}-b^{2}-\left(9a-2b\right)\left(4a+3b\right)$$

Calculate 6 to the power of 2 and get 36.

$$36a^{2}-b^{2}-\left(9a-2b\right)\left(4a+3b\right)$$

Apply the distributive property by multiplying each term of 9a-2b by each term of 4a+3b.

$$36a^{2}-b^{2}-\left(36a^{2}+27ab-8ba-6b^{2}\right)$$

Combine 27ab and -8ba to get 19ab.

$$36a^{2}-b^{2}-\left(36a^{2}+19ab-6b^{2}\right)$$

To find the opposite of 36a^{2}+19ab-6b^{2}, find the opposite of each term.

$$36a^{2}-b^{2}-36a^{2}-19ab-\left(-6b^{2}\right)$$

The opposite of -6b^{2} is 6b^{2}.

$$36a^{2}-b^{2}-36a^{2}-19ab+6b^{2}$$

Combine 36a^{2} and -36a^{2} to get 0.

$$-b^{2}-19ab+6b^{2}$$

Combine -b^{2} and 6b^{2} to get 5b^{2}.

$$5b^{2}-19ab$$