Question

What must be added to $16X^2+25Y^2$ to make it a square of a binomial?

• A. $-40$xy
• B. $40$xy
• C. $44$xy
• D. $-44$xy

Answer 1

Answer: (A), (B)

The correct options are
A $-40$xy
B $40$xy

$16x^2+25y^2$

$=(4x{)}^2+(5y{)}^2+\left(\alpha \right)\leftarrow$ for perfect square of binomial

using

$(a+b{)}^2=a^2+b^2+2ab$ $a=4x$

and $(a-b{)}^2=a^2+b^2-2ab$ $b=5y$

For perfect square

$\alpha =2ab$

$\alpha =2\left(4x\right)\left(5y\right)$

$=40xy$

Or

$\alpha =-2b$

$\alpha =-2\left(4x\right)\left(5y\right)$

$-40xy$

$\therefore$ (A) and (B)