Complete the following exercise: $$ (\sqrt{x}+\frac{1}{2})(\sqrt{x}-\frac{1}{2})=0 $$

$$ \sqrt{\frac{1}{2}} $$

Multiplication of the sum of two elements 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.

Detailed explanation

Start practice

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

Solve:

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

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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: