Answer:
B) ( x + 3y)²
Step-by-step explanation:
u = x + y ; v = x + 5y
uv = ( x + y ) * ( x + 5y)
= x * ( x + 5y) + y * (x + 5y) [ x * ( x + 5y) = x*x + x*5y = x² + 5xy]
= x² + 5xy + xy + 5y²
uv = x² + 6xy + 5y²----------equ 1
v - u = x + 5y - ( x+y)
= x + 5y - x - y
= 4y
(v-u)² = (4y)² = 16y²
[(v-u)/2]² = 16y² / 2²
= 16y² / 4 = 4y²
[(v-u)/2]² = 4y² ----------- equ 2
uv + [(v-u)/2]² = x² + 6xy + 5y² + 4y² ( from equ 1 and equ 2)
= x² + 6xy + 9y²
= ( x + 3y)²
