Question

What is the answer to this problem work included please

Answer 1

B) ( x + 3y)²

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