Solve 4 its value wher ( b ) Simplify : (1/3 * x ^ 2 - 8y) * i and (1/3 * x ^ 2 + 8y) A Also , find its value when x = 1 and y = 3 ( c) | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$\quad ( \frac { 1 } { 3 } x ^ { 2 } - 8 y ) ( \frac { 1 } { 3 } x ^ { 2 } + 8 y ) . x = 1 y = 3$$

Evaluate

$\frac{x^{4}}{9}-64y^{2}$

Solution Steps

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

$$\left(\frac{1}{3}x^{2}\right)^{2}-\left(8y\right)^{2}$$

Expand $\left(\frac{1}{3}x^{2}\right)^{2}$.

$$\left(\frac{1}{3}\right)^{2}\left(x^{2}\right)^{2}-\left(8y\right)^{2}$$

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

$$\left(\frac{1}{3}\right)^{2}x^{4}-\left(8y\right)^{2}$$

Calculate $\frac{1}{3}$ to the power of $2$ and get $\frac{1}{9}$.

$$\frac{1}{9}x^{4}-\left(8y\right)^{2}$$

Expand $\left(8y\right)^{2}$.

$$\frac{1}{9}x^{4}-8^{2}y^{2}$$

Calculate $8$ to the power of $2$ and get $64$.

$$\frac{1}{9}x^{4}-64y^{2}$$

Expand

$\frac{x^{4}}{9}-64y^{2}$

Solution Steps

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

$$\left(\frac{1}{3}x^{2}\right)^{2}-\left(8y\right)^{2}$$

Expand $\left(\frac{1}{3}x^{2}\right)^{2}$.

$$\left(\frac{1}{3}\right)^{2}\left(x^{2}\right)^{2}-\left(8y\right)^{2}$$

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

$$\left(\frac{1}{3}\right)^{2}x^{4}-\left(8y\right)^{2}$$

Calculate $\frac{1}{3}$ to the power of $2$ and get $\frac{1}{9}$.

$$\frac{1}{9}x^{4}-\left(8y\right)^{2}$$

Expand $\left(8y\right)^{2}$.

$$\frac{1}{9}x^{4}-8^{2}y^{2}$$

Calculate $8$ to the power of $2$ and get $64$.

$$\frac{1}{9}x^{4}-64y^{2}$$