Question

Simplify: $18xy(16x^2-25y^2)÷3xy(4x+5y)$

• A. $\frac{6}{4x+5y}$
• B. $4x+5y$
• C. $4x-5y$
• D. $6(4x-5y)$

Answer 1

Answer: (D)

$6(4x-5y)$

$18xy(16x^2-25y^2)÷3xy(4x+5y)$

$=\frac{18xy(16x^2-25y^2)}{3xy(4x+5y)}=\frac{6[{\left(4x\right)}^2-{\left(5y\right)}^2]}{(4x+5y)}$

$=\frac{6(4x-5y)(4x+5y)}{(4x+5y)}$ ...$(\because a^2-b^2=(a-b)(a+b))$

$=6(4x-5y)$