Simplify (x + √x)²: Expanding a Binomial with Square Root

Question

Simply the following expression:

$(x+\sqrt{x})^2$

00:00 Simply

00:03 We'll use the abbreviated multiplication formulas to open the parentheses

00:11 We'll use this formula in our exercise where X equals A

00:20 and the root of X is B

00:24 We'll substitute according to the formula

00:42 A square root squared equals the number itself

00:50 We'll factor X squared into factors X and X

00:56 We'll find a common factor and take it out of the parentheses

01:04 And this is the solution to the question

To solve the problem, we undertake the following steps:

Identify the components $a = x$ and $b = \sqrt{x}$ in the expression $(x + \sqrt{x})^2$ .
Apply the square of sum formula: $(a + b)^2 = a^2 + 2ab + b^2$ .
Substitute the values:
- $a^2 = x^2$
- $2ab = 2 \times x \times \sqrt{x} = 2x\sqrt{x}$
- $b^2 = (\sqrt{x})^2 = x$
Simplifying gives: $x^2 + 2x\sqrt{x} + x$
Recognize that this can be factored to yield: $x(x + 2\sqrt{x} + 1)$

Thus, the simplified expression is $\boxed{x[x + 2\sqrt{x} + 1]}$ .

$x\lbrack x+2\sqrt{x}+1\rbrack$