Solve (10x + 1/2 * y)(10x - 1/2 * y) | 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

$$(10x+\frac{1}{2}y)(10x-\frac{1}{2}y)$$

Evaluate

$-\frac{y^{2}}{4}+100x^{2}$

Solution Steps

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

$$\left(10x\right)^{2}-\left(\frac{1}{2}y\right)^{2}$$

Expand $\left(10x\right)^{2}$.

$$10^{2}x^{2}-\left(\frac{1}{2}y\right)^{2}$$

Calculate $10$ to the power of $2$ and get $100$.

$$100x^{2}-\left(\frac{1}{2}y\right)^{2}$$

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

$$100x^{2}-\left(\frac{1}{2}\right)^{2}y^{2}$$

Calculate $\frac{1}{2}$ to the power of $2$ and get $\frac{1}{4}$.

$$100x^{2}-\frac{1}{4}y^{2}$$

Expand

$-\frac{y^{2}}{4}+100x^{2}$

Solution Steps

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

$$\left(10x\right)^{2}-\left(\frac{1}{2}y\right)^{2}$$

Expand $\left(10x\right)^{2}$.

$$10^{2}x^{2}-\left(\frac{1}{2}y\right)^{2}$$

Calculate $10$ to the power of $2$ and get $100$.

$$100x^{2}-\left(\frac{1}{2}y\right)^{2}$$

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

$$100x^{2}-\left(\frac{1}{2}\right)^{2}y^{2}$$

Calculate $\frac{1}{2}$ to the power of $2$ and get $\frac{1}{4}$.

$$100x^{2}-\frac{1}{4}y^{2}$$