Solve [3a(2a+b)+5ab]:{[3a^{2}b^2-a^2b^2(-5a)]:(-2ab)^2}

$$[ 3 a ( 2 a + b ) + 5 a b ] : \{ [ 3 a ^ { 2 } b ^ { 2 } - a ^ { 2 } b ^ { 2 } ( - 5 a ) ] : ( - 2 a b ) ^ { 2 } \}$$

Evaluate

$$\frac{8a\left(3a+4b\right)}{5a+3}$$

Short Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

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

Expand \left(-2ab\right)^{2}.

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

Calculate -2 to the power of 2 and get 4.

$$\frac{3a\left(2a+b\right)+5ab}{\frac{3a^{2}b^{2}-a^{3}b^{2}\left(-5\right)}{4a^{2}b^{2}}}$$

Factor the expressions that are not already factored in \frac{3a^{2}b^{2}-a^{3}b^{2}\left(-5\right)}{4a^{2}b^{2}}.

$$\frac{3a\left(2a+b\right)+5ab}{\frac{\left(5a+3\right)a^{2}b^{2}}{4a^{2}b^{2}}}$$

Cancel out a^{2}b^{2} in both numerator and denominator.

$$\frac{3a\left(2a+b\right)+5ab}{\frac{5a+3}{4}}$$

Divide 3a\left(2a+b\right)+5ab by \frac{5a+3}{4} by multiplying 3a\left(2a+b\right)+5ab by the reciprocal of \frac{5a+3}{4}.

$$\frac{\left(3a\left(2a+b\right)+5ab\right)\times 4}{5a+3}$$

Use the distributive property to multiply 3a by 2a+b.

$$\frac{\left(6a^{2}+3ab+5ab\right)\times 4}{5a+3}$$

Combine 3ab and 5ab to get 8ab.

$$\frac{\left(6a^{2}+8ab\right)\times 4}{5a+3}$$

Use the distributive property to multiply 6a^{2}+8ab by 4.

$$\frac{24a^{2}+32ab}{5a+3}$$

Expand

$$\frac{8\left(3a^{2}+4ab\right)}{5a+3}$$

Short Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

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

Expand \left(-2ab\right)^{2}.

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

Calculate -2 to the power of 2 and get 4.

$$\frac{3a\left(2a+b\right)+5ab}{\frac{3a^{2}b^{2}-a^{3}b^{2}\left(-5\right)}{4a^{2}b^{2}}}$$

Factor the expressions that are not already factored in \frac{3a^{2}b^{2}-a^{3}b^{2}\left(-5\right)}{4a^{2}b^{2}}.

$$\frac{3a\left(2a+b\right)+5ab}{\frac{\left(5a+3\right)a^{2}b^{2}}{4a^{2}b^{2}}}$$

Cancel out a^{2}b^{2} in both numerator and denominator.

$$\frac{3a\left(2a+b\right)+5ab}{\frac{5a+3}{4}}$$

Divide 3a\left(2a+b\right)+5ab by \frac{5a+3}{4} by multiplying 3a\left(2a+b\right)+5ab by the reciprocal of \frac{5a+3}{4}.

$$\frac{\left(3a\left(2a+b\right)+5ab\right)\times 4}{5a+3}$$

Use the distributive property to multiply 3a by 2a+b.

$$\frac{\left(6a^{2}+3ab+5ab\right)\times 4}{5a+3}$$

Combine 3ab and 5ab to get 8ab.

$$\frac{\left(6a^{2}+8ab\right)\times 4}{5a+3}$$

Use the distributive property to multiply 6a^{2}+8ab by 4.

$$\frac{24a^{2}+32ab}{5a+3}$$