Question

What should be added to
$49x {}^{2} + 24xy + 16y {}^{2}$
to make it a perfect square​

Answer 1

$28xy \: should \: be \: added \: \\ \\ bcoz \\ \\ 49 {x}^{2} + 24xy + 16 {y}^{2} \\ \\ \\ \\ \\ = {(7x)}^{2} + 2(7x)(4y) + {(4y)}^{2} \\ = {(7x + 4y)}^{2} \\ it \: s \: a \: perfect \: square \: but \: 2(7x)(4y) = 56xy \\ \\ but \: in \: question \: it \: is \: 24xy \\ \\ so \: 56xy - 24xy = 28xy$

Hence, 28xy should be added to make it a perfect square