Question

Use factorisation method:

$\sqrt{(a^2-25)(a^2+8a+15)(a^2-2a-15)}$

• A. $(a+5)(a-5)(a+3)$
• B. $\left|\right(a+5{)}^2(a-5)(a+3)|$
• C. $\left|\right(a+5\left)\right(a-5\left)\right(a+3\left)\right|$
• D. $(a^2-5^2)(a+3)$

Answer 1

The correct option is C $\left|\right(a+5\left)\right(a-5\left)\right(a+3\left)\right|$

$\sqrt{(a^2-25)(a^2+8a+15)(a^2-2a-15)}$

Factor of $a^2-25=(a+5)(a-5)$

Factor of $a^2+8a+15=(a+3)(a+5)$

Factor of $a^2-2a-15=(a-5)(a+3)$

Therefore, $\sqrt{(a^2-25)(a^2+8a+15)(a^2-2a-15)}=\sqrt{(a+5{)}^2(a-5{)}^2(a+3{)}^2}$

$=$ $\sqrt{\left(\right(a+5\left)\right(a-5\left)\right(a+3){)}^2}$

$=$ $\left|\right(a+5\left)\right(a-5\left)\right(a+3\left)\right|$