Factorise (x+2)^2 + 5(x+2)
Answers
Answer:
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Step-by-step explanation:
First, rewrite the term on the left as:
(
x
+
2
)
(
x
+
2
)
−
5
(
x
−
2
)
Next, factor out a common term of
(
x
−
2
)
giving:
(
(
x
+
2
)
−
5
)
(
x
−
2
)
⇒
(
x
+
2
−
5
)
(
x
−
2
)
⇒
(
x
−
3
)
(
x
−
2
)
Answer link
Fabio
Mar 17, 2018
(
x
−
3
)
(
x
+
2
)
Explanation:
First we expand the
(
x
+
2
)
2
which looks like
(
x
+
2
)
(
x
+
2
)
Next we just multiply it out which will give us
x
2
+
4
x
+
4
Now that we know
(
x
+
2
)
2
=
x
2
+
4
x
+
4
We can do the other part which is
5
(
x
+
2
)
Which is
(
5
x
+
10
)
Now we know
5
(
x
+
2
)
=
(
5
x
+
10
)
Now we can write the problem out expanded
x
2
+
4
x
+
4
−
(
5
x
+
10
)
NOTICE THE NEGATIVE SIGN IN FRONT OF THE PARENTHESES.
We have to distribute this negative to all terms in the parentheses.
Which gives us
x
2
+
4
x
+
4
−
5
x
−
10
Now we just combine like terms
x
2
−
1
x
−
6
Now we need 2 numbers that multiply to
−
6
and add up to
−
1
These numbers are
−
3
and
2
Notice
−
3
⋅
2
=
−
6
And
−
3
+
2
=
−
1
So we then get
(
x
−
3
)
(
x
+
2
)
Factor
x
+
2
out of
(
x
+
2
)
2
.
(
x
+
2
)
(
x
+
2
)
−
5
(
x
+
2
)
Factor
x
+
2
out of
−
5
(
x
+
2
)
.
(
x
+
2
)
(
x
+
2
)
+
(
x
+
2
)
⋅
−
5
Factor
x
+
2
out of
(
x
+
2
)
(
x
+
2
)
+
(
x
+
2
)
⋅
−
5
.
(
x
+
2
)
(
x
+
2
−
5
)