Factorize (x + y) (ax — ay)
A. (x — y)(1 — a)
B. (x + y)(1 + a)
C. (x + y)(1 — a)
D. (x — y)(1 + a)
The correct factorization is:
(x + y)(ax - ay) = x(ax - ay) + y(ax - ay) = ax^2 - axy + axy - ay^2 = ax^2 - ay^2
Therefore, the correct option is:
D. (x - y)(1 + a)
To factorize the expression (x + y)(ax - ay), we can use the distributive property.
First, distribute (ax - ay) to both terms inside the first parentheses:
(x + y)(ax) - (x + y)(ay)
Next, simplify each of these terms:
= ax^2 + xy - axy - ay^2
Now, combine like terms:
= ax^2 - axy + xy - ay^2
Finally, factor out common terms:
= a(x^2 - xy) + y(x - y)
Therefore, the factorization of (x + y)(ax - ay) is:
= a(x^2 - xy) + y(x - y)
So, the correct answer is not provided among the options.