How to solve (5x+10y)(5x-10y)

1. Factor the equation (x + 2)(x + 3) = 0. 2. Set each factor equal to zero: x + 2 = 0 and x + 3 = 0. 3. Solve for x: x = -2 and x = -3.

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Question

$$(5x+10y)(5x-10y)$$

Evaluate

$25\left(x^{2}-4y^{2}\right)$

Solution Steps

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

$$\left(5x\right)^{2}-\left(10y\right)^{2}$$

Expand $\left(5x\right)^{2}$.

$$5^{2}x^{2}-\left(10y\right)^{2}$$

Calculate $5$ to the power of $2$ and get $25$.

$$25x^{2}-\left(10y\right)^{2}$$

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

$$25x^{2}-10^{2}y^{2}$$

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

$$25x^{2}-100y^{2}$$

Show Solution

Expand

$25x^{2}-100y^{2}$

Solution Steps

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

$$\left(5x\right)^{2}-\left(10y\right)^{2}$$

Expand $\left(5x\right)^{2}$.

$$5^{2}x^{2}-\left(10y\right)^{2}$$

Calculate $5$ to the power of $2$ and get $25$.

$$25x^{2}-\left(10y\right)^{2}$$

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

$$25x^{2}-10^{2}y^{2}$$

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

$$25x^{2}-100y^{2}$$

Show Solution

Basic Math

Pre-Algebra

Algebra

Trigonometry

Calculus

Precalculus

Statistics

Finite Math

Linear Algebra

Chemistry

Example

Question

Evaluate

Solution Steps

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Solution Steps