# Multiplication of the sum of two elements by the difference between them

🏆Practice multiplication of the sum of two terms by the difference between them

$(X + Y)\times (X - Y) = X^2 - Y^2$

This is one of the shortened multiplication formulas.

As can be seen, this formula can be used when there is a multiplication between the sum of two particular elements and the subtraction between the two elements.
Instead of presenting them as a multiplication of sum and subtraction, it can be written $X^2 - Y^2$ and it expresses exactly the same thing. In the same way, if such an expression $X^2 - Y^2$ representing the subtraction of two squared numbers is presented to you, you can write it like this: $(X + Y)\times (X - Y)$
Pay attention: the formula works both in non-algebraic expressions and in expressions that combine unknowns and numbers.

## Test yourself on multiplication of the sum of two terms by the difference between them!

Solve:

$$(2+x)(2-x)=0$$

## Let's look at an example

If we are given: $(x+4)(x-4)$
We can see that we are referring to a multiplication between the sum of two elements and the difference between them.
Therefore, we can present the same expression according to the formula in the following way:
$x^2-4^2$
$x^2-16$
In the same way, if we were given the expression:
$x^2-16$
We could express $16$ as a squared number, that is $4^2$,
Obtain a representation that fits the formula:
$x^2-4^2$
From here using the formula and presenting the expression in the following way:

$x^2-4^2=(X-4)(x+4)$

If you are interested in this article, you might also be interested in the following articles:

The formula for the difference of squares

The formula for the sum of squares

The formulas that refer to two expressions to the power of 3

In the blog of Tutorela you will find a variety of articles about mathematics.

## Examples and exercises with solutions for multiplying the sum of two elements by the difference between them

### Exercise #1

Solve:

$(2+x)(2-x)=0$

### Step-by-Step Solution

We use the abbreviated multiplication formula:

$4-x^2=0$

We isolate the terms and extract the root:

$4=x^2$

$x=\sqrt{4}$

$x=\pm2$

±2

### Exercise #2

$(2x)^2-3=6$

### Step-by-Step Solution

We move the sections and equal to 0

$4x^2-3-6=0$

$4x^2-9=0$

We use the shortcut multiplication formula:

$4(x^2-\frac{9}{4})=0$

$x^2-(\frac{3}{2})^2=0$

$(x-\frac{3}{2})(x+\frac{3}{2})=0$

$x=\pm\frac{3}{2}$

$±\frac{3}{2}$

### Exercise #3

Complete the following exercise:

$(\sqrt{x}+\frac{1}{2})(\sqrt{x}-\frac{1}{2})=0$

### Video Solution

$\frac{1}{4}$

### Exercise #4

Solve the exercise:

$(x+3)(x-3)+(x+1)(x-1)=0$

### Video Solution

$±\sqrt{5}$

### Exercise #5

Fill in the missing element to obtain a true expression:

$(x+_—)\cdot(x-_—)=x^2-121$