Question

can anybody solve I need help


The factorisation of a(x+y+z)+b(x+y+z)+c(x+y+z) is

(a+b+c)(xy+yz+zx)
(ab+bc+ca)(x+y+z)
(a+b+c)(x+y+z)
none of the above


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Answer 1

(a + b + c)(x + y+ z)

There are two ways to understand this. The first one is:

➡ a(x +y + z)+b(x + y + z)+c(x + y + z)

We can see that (x + y + z) is common in all there of them. So, if we take them out, we are left with a + b + c and this can be written as:

(x + y + z) (a + b + c).

➡ The next method is a bit more complicated and is the algebraic method of coming at the conclusion.

a(x +y + z)+b(x + y + z)+c(x + y + z)

Opening the brackets:

ax + ay + az + bx + by + bz + cx + cy + cz

Now, re-arranging:

ax + bx + cx + ay + by + cy + az + bz + cz

Bracketing:

(ax + bx + cx) + (ay + by + cy) + (az + bz + cz)

We can see that x, y and z are the common variables in the three sets in order. So taking them out:

(x + y + z) (a + b + c)

(The first method would be appropriate in solving the question quickly and the second method is the actual algebraic expansion for understanding the concept.)