Question

Let's find the G.C.D of the following Algebraic expressions:

1. x²+xy, xz+yz, x²+2xy+y²

2. a²-b²-c²+2bc, b²-c²-a²+2ac, c²-a²-b²+2ab

3. 6x²-13xa+6a, 6x²+11xa-10a², 6x²+2xa-4a²

Solve these sums please
​

Answer 1

Answer:

Factors of x2 + xy=x(x + y)

Factors of xz + yz=z(x + y)

Factors of x2 + 2xy + y2=(x + y)2 … (from properties of (a + b)2)

GCD is the greatest common divisor, which is equal to the product of all the common divisors.

∴ the GCD of x2 + xy,xz + yz, x2 + 2xy + y2 is (x + y)