Simplify the expression: (sqrt(5) − 3)(sqrt(20) + 3) - sqrt(5)(sqrt(20) + 3) − 3(sqrt(20) + 3)

Question

ScanSolve AI Tutor · Accepted Answer

Alright Intellectual, let's simplify this expression.

The expression is:

(\sqrt{5} - 3)(\sqrt{20} + 3) - \sqrt{5}(\sqrt{20} + 3) - 3(\sqrt{20} + 3)

Identify the common factor.
Notice that $(\sqrt{20} + 3)$ is a common factor in all three terms. Factor it out.
$(\sqrt{20} + 3) [(\sqrt{5} - 3) - \sqrt{5} - 3]$
Simplify the terms inside the square bracket.
$\sqrt{5} - 3 - \sqrt{5} - 3$
Combine the $\sqrt{5}$ terms and the constant terms.
$(\sqrt{5} - \sqrt{5}) + (-3 - 3)$ $0 - 6$ $-6$
Substitute the simplified bracket back into the expression.
$(\sqrt{20} + 3) \times (-6)$
Simplify $\sqrt{20}$ .
$\sqrt{20} = \sqrt{4 \times 5} = \sqrt{4} \times \sqrt{5} = 2\sqrt{5}$
Substitute the simplified surd back into the expression and distribute.
$(2\sqrt{5} + 3) \times (-6)$ $-6 \times 2\sqrt{5} + (-6) \times 3$ $-12\sqrt{5} - 18$
The simplified expression in surd form is:
$\boxed{-18 - 12\sqrt{5}}$

Simplify the expression: (sqrt(5) - 3)(sqrt(20) + 3) - sqrt(5)(sqrt(20) + 3) - 3(sqrt(20) + 3)