How to solve (2x-y+3)(2x-y-3)

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

$$(2x-y+3)(2x-y-3)$$

Evaluate

$\left(2x-y\right)^{2}-9$

Solution Steps

Multiplication can be transformed into difference of squares using the rule: $\left(a-b\right)\left(a+b\right)=a^{2}-b^{2}$, where $a=2x-y$ and $b=3$.

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

Use binomial theorem $\left(a-b\right)^{2}=a^{2}-2ab+b^{2}$ to expand $\left(2x-y\right)^{2}$.

$$4x^{2}-4xy+y^{2}-3^{2}$$

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

$$4x^{2}-4xy+y^{2}-9$$

Show Solution

Expand

$4x^{2}-4xy+y^{2}-9$

Solution Steps

Multiplication can be transformed into difference of squares using the rule: $\left(a-b\right)\left(a+b\right)=a^{2}-b^{2}$, where $a=2x-y$ and $b=3$.

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

Use binomial theorem $\left(a-b\right)^{2}=a^{2}-2ab+b^{2}$ to expand $\left(2x-y\right)^{2}$.

$$4x^{2}-4xy+y^{2}-3^{2}$$

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

$$4x^{2}-4xy+y^{2}-9$$

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