Solve -5a*(2a+b)-2b*(a-6b)+(3a+b)*(3a-b)

$$- 5 a \cdot ( 2 a + b ) - 2 b \cdot ( a - 6 b ) + ( 3 a + b ) \cdot ( 3 a - b )$$

Evaluate

$$11b^{2}-7ab-a^{2}$$

Solution Steps

Use the distributive property to multiply -5a by 2a+b.

$$-10a^{2}-5ab-2b\left(a-6b\right)+\left(3a+b\right)\left(3a-b\right)$$

Consider \left(3a+b\right)\left(3a-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}.

$$-10a^{2}-5ab-2b\left(a-6b\right)+\left(3a\right)^{2}-b^{2}$$

Expand \left(3a\right)^{2}.

$$-10a^{2}-5ab-2b\left(a-6b\right)+3^{2}a^{2}-b^{2}$$

Calculate 3 to the power of 2 and get 9.

$$-10a^{2}-5ab-2b\left(a-6b\right)+9a^{2}-b^{2}$$

Use the distributive property to multiply -2b by a-6b.

$$-10a^{2}-5ab-2ba+12b^{2}+9a^{2}-b^{2}$$

Combine -5ab and -2ba to get -7ab.

$$-10a^{2}-7ab+12b^{2}+9a^{2}-b^{2}$$

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

$$-a^{2}-7ab+12b^{2}-b^{2}$$

Combine 12b^{2} and -b^{2} to get 11b^{2}.

$$-a^{2}-7ab+11b^{2}$$

Expand

$$11b^{2}-7ab-a^{2}$$

Solution Steps

Use the distributive property to multiply -5a by 2a+b.

$$-10a^{2}-5ab-2b\left(a-6b\right)+\left(3a+b\right)\left(3a-b\right)$$

Consider \left(3a+b\right)\left(3a-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}.

$$-10a^{2}-5ab-2b\left(a-6b\right)+\left(3a\right)^{2}-b^{2}$$

Expand \left(3a\right)^{2}.

$$-10a^{2}-5ab-2b\left(a-6b\right)+3^{2}a^{2}-b^{2}$$

Calculate 3 to the power of 2 and get 9.

$$-10a^{2}-5ab-2b\left(a-6b\right)+9a^{2}-b^{2}$$

Use the distributive property to multiply -2b by a-6b.

$$-10a^{2}-5ab-2ba+12b^{2}+9a^{2}-b^{2}$$

Combine -5ab and -2ba to get -7ab.

$$-10a^{2}-7ab+12b^{2}+9a^{2}-b^{2}$$

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

$$-a^{2}-7ab+12b^{2}-b^{2}$$

Combine 12b^{2} and -b^{2} to get 11b^{2}.

$$-a^{2}-7ab+11b^{2}$$