factorise : a.144(a-b)²-169(a+b)²
and b. x²+16x+60
Answers
Step-by-step explanation:
This is a difference of two squares so it factors as
(
a
−
b
)
(
a
+
b
)
, where a and b are the square roots of the original expression. See proofs below.
Warning: Differences of squares only works when there is a minus between the two terms, and doesn't work if it is positive. A sum of squares can't be factored with real numbers
x
2
−
169
=
(
x
+
13
)
(
x
−
13
)
, since
x
∙
x
=
x
2
and
13
∙
−
13
=
−
169
.
x
2
−
169
=
(
x
+
13
)
(
x
−
13
)
Below are a few exercises to practice yourself. Watch out for the trick question(s) near the end!!:)
Factor each expression completely
a)
x
2
−
49
b)
4
x
2
−
81
c)
x
2
+
25
d)
x
4
−
16
Hopefully this helps. Best of luck in the future!
Answer link
Jacobi J.
Jun 30, 2018
(
x
+
13
)
(
x
−
13
)
Explanation:
What we have is a difference of squares, which has the form
a
2
−
b
2
, where
a
and
b
are perfect squares, which factor as
(
a
+
b
)
(
a
−
b
)
In our example,
a
=
x
2
, and
b
=
√
169
, or
b
=
13
. We can plug this into our difference of squares expansion equation to get
Answer:
(i) (-1) (a+25b) (25a+b) or (-a-25b) (25a+b)
(ii) (x+5) (x+12)