Question

Find the factors of a² + ab +bc + ca​

Answer 1

Given:

The expression -

$\underline{\boxed{ \bf \longmapsto \: a^2 + ab + bc + ca \:}}$

What To Find:

We have to find

• The factors of the given expressions.

How To Find:

To find it, we have to,

• Use the regrouping method.
• First, regroup the terms according.
• Next, find the common factors in each group.
• Then, factorize the expression further.

Solution:

$\sf \longmapsto \: a^2 + ab + bc + ca$

Regroup and rearrange the terms,

$\sf \longmapsto \: \underline{a^2 + ab} + \underline{bc + ca}$

Here,

• First group:- $\sf a^2 + ab$

• Second group:- $\sf bc + ca$

Take out the common factor in the first group,

$\sf \longmapsto \: \underline{a(a + b)} + bc + ca$

Take out the common factor in the second group,

$\sf \longmapsto \: a(a + b) + \underline{c(a + b)}$

Now, inside of the brackets are same, so take them as common,

$\sf \longmapsto \: (a + b) + a + c$

Take a + c as one term,

$\sf \longmapsto \: (a + b) + (a + c)$

Final Answer:

∴ Thus, the factors are (a + b) and (a + c).