Solve -3b(-a-3b)+(a-3b)(a+3b)+(a-3b)(3b-a)+a^2+9b^2

$$- 3 b ( - a - 3 b ) + ( a - 3 b ) ( a + 3 b ) + ( a - 3 b ) ( 3 b - a ) + a ^ { 2 } + 9 b ^ { 2 }$$

Evaluate

$$a\left(a+9b\right)$$

Solution Steps

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

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

Multiply -3 and -1 to get 3.

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

Consider \left(a-3b\right)\left(a+3b\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

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

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

Calculate 3 to the power of 2 and get 9.

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

Combine 9b^{2} and -9b^{2} to get 0.

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

Use the distributive property to multiply a-3b by 3b-a and combine like terms.

$$3ba+a^{2}+6ab-a^{2}-9b^{2}+a^{2}+9b^{2}$$

Combine 3ba and 6ab to get 9ba.

$$9ba+a^{2}-a^{2}-9b^{2}+a^{2}+9b^{2}$$

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

$$9ba-9b^{2}+a^{2}+9b^{2}$$

Combine -9b^{2} and 9b^{2} to get 0.

$$9ba+a^{2}$$

Expand

$$a^{2}+9ab$$

Solution Steps

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

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

Multiply -3 and -1 to get 3.

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

Consider \left(a-3b\right)\left(a+3b\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

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

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

Calculate 3 to the power of 2 and get 9.

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

Combine 9b^{2} and -9b^{2} to get 0.

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

Use the distributive property to multiply a-3b by 3b-a and combine like terms.

$$3ba+a^{2}+6ab-a^{2}-9b^{2}+a^{2}+9b^{2}$$

Combine 3ba and 6ab to get 9ba.

$$9ba+a^{2}-a^{2}-9b^{2}+a^{2}+9b^{2}$$

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

$$9ba-9b^{2}+a^{2}+9b^{2}$$

Combine -9b^{2} and 9b^{2} to get 0.

$$9ba+a^{2}$$