How to solve (5a+3b)(5a-3b)

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

$$(5a+3b)(5a-3b)$$

Evaluate

$25a^{2}-9b^{2}$

Solution Steps

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

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

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

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

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

$$25a^{2}-\left(3b\right)^{2}$$

Expand $\left(3b\right)^{2}$.

$$25a^{2}-3^{2}b^{2}$$

Calculate $3$ to the power of $2$ and get $9$.

$$25a^{2}-9b^{2}$$

Show Solution

Expand

$25a^{2}-9b^{2}$

Solution Steps

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

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

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

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

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

$$25a^{2}-\left(3b\right)^{2}$$

Expand $\left(3b\right)^{2}$.

$$25a^{2}-3^{2}b^{2}$$

Calculate $3$ to the power of $2$ and get $9$.

$$25a^{2}-9b^{2}$$

Show Solution

Basic Math

Pre-Algebra

Algebra

Trigonometry

Calculus

Precalculus

Statistics

Finite Math

Linear Algebra

Chemistry

Example

Question

Evaluate

Solution Steps

Expand

Solution Steps