Question

factorise each of the following:
3x+6
5xy+10x​

Answer 1

a) 3x+6

=3(x+2)

b) 5xy+10x

= 5x(y+2)

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Answer 2

Answer: 1. 3(x + 2) 2. 5x(y + 2)

Step-by-step explanation:

So lets start off with bit one:

1. 3x + 6

See, whenever you need to factorise a given expression, the first thing you need to do is to find the HCF.

So lets look at the given expression 3x + 6.

Observe the numerical coefficients 3 and 6.

We see that 3 is the highest common factor of 3 and 6.

Other than that, we see that no number divides the two terms 3x and 6 completely.

So how do we factorise once we know the HCF?

Well, its simple. Just divide the 2 terms by the HCF, 3.

Now, 3x / 3 = x

and 6/3 = 2.

Now, on simplifying, we get x + 2.

But we need to write 3x + 6 in such a way that the answer on both LHS and RHS is the same.

Now, from the above we can conclude that 3 × (x + 2) = 3x + 6.

So we can rewrite it as 3(x + 2) = 3x + 6.

2. 5xy + 10x

Lets figure out the HCF first.

Here we see that 5 divides both 5xy and 10x.

However there's another variable which divides the two terms, that is x.

So our HCF becomes 5 × x = 5x.

Now, lets divide the expression by 5x.

5xy ÷ 5x gives us y.

10x ÷ 5x gives us 2.

So we can conclude that 5 × (y + 2) = 5xy + 10x.

This can be written as 5(y + 2).

Hope it helps....

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