Solve a+b/6a-b/2aa^2+b^2/3b^2=

$$\frac { a + b } { 6 } \frac { a - b } { 2 a } \frac { a ^ { 2 } + b ^ { 2 } } { 3 b ^ { 2 } } =$$

Evaluate

$$\frac{a^{4}-b^{4}}{36ab^{2}}$$

Short Solution Steps

Multiply \frac{a+b}{6} times \frac{a-b}{2a} by multiplying numerator times numerator and denominator times denominator.

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

Multiply \frac{\left(a+b\right)\left(a-b\right)}{6\times 2a} times \frac{a^{2}+b^{2}}{3b^{2}} by multiplying numerator times numerator and denominator times denominator.

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

Multiply 6 and 2 to get 12.

$$\frac{\left(a+b\right)\left(a-b\right)\left(a^{2}+b^{2}\right)}{12a\times 3b^{2}}$$

Multiply 12 and 3 to get 36.

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

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

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

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

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

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\frac{a^{4}-\left(b^{2}\right)^{2}}{36ab^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\frac{a^{4}-b^{4}}{36ab^{2}}$$

Expand

$$-\frac{b^{4}-a^{4}}{36ab^{2}}$$

Short Solution Steps

Multiply \frac{a+b}{6} times \frac{a-b}{2a} by multiplying numerator times numerator and denominator times denominator.

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

Multiply \frac{\left(a+b\right)\left(a-b\right)}{6\times 2a} times \frac{a^{2}+b^{2}}{3b^{2}} by multiplying numerator times numerator and denominator times denominator.

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

Multiply 6 and 2 to get 12.

$$\frac{\left(a+b\right)\left(a-b\right)\left(a^{2}+b^{2}\right)}{12a\times 3b^{2}}$$

Multiply 12 and 3 to get 36.

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

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

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

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

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

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\frac{a^{4}-\left(b^{2}\right)^{2}}{36ab^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\frac{a^{4}-b^{4}}{36ab^{2}}$$