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

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

Evaluate

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

Solution Steps

Multiply 2 and 3 to get 6.

$$6a\left(a-b\right)-\left(2a+3b\right)\left(2a-3b\right)+6ab$$

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

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

Consider \left(2a+3b\right)\left(2a-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}.

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

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

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

Calculate 2 to the power of 2 and get 4.

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

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

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

Calculate 3 to the power of 2 and get 9.

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

To find the opposite of 4a^{2}-9b^{2}, find the opposite of each term.

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

The opposite of -9b^{2} is 9b^{2}.

$$6a^{2}-6ab-4a^{2}+9b^{2}+6ab$$

Combine 6a^{2} and -4a^{2} to get 2a^{2}.

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

Combine -6ab and 6ab to get 0.

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

Expand

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

Solution Steps

Multiply 2 and 3 to get 6.

$$6a\left(a-b\right)-\left(2a+3b\right)\left(2a-3b\right)+6ab$$

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

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

Consider \left(2a+3b\right)\left(2a-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}.

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

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

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

Calculate 2 to the power of 2 and get 4.

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

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

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

Calculate 3 to the power of 2 and get 9.

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

To find the opposite of 4a^{2}-9b^{2}, find the opposite of each term.

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

The opposite of -9b^{2} is 9b^{2}.

$$6a^{2}-6ab-4a^{2}+9b^{2}+6ab$$

Combine 6a^{2} and -4a^{2} to get 2a^{2}.

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

Combine -6ab and 6ab to get 0.

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