Prepare a chart showing different methods of factorising algebraic expressions. Give one example for each method.
Answers
Answer:
Prepare a chart showing different methods of factorising algebraic expressions. Give one example for each method.
HERE'S YOUR ANSWER BUDDY...
ANSWER:
Method 1:
Highest Common Factor Method
2
x
2
+
4
x
Follow the steps given below to find the factors of the expression.
Step 1:
2
x
2
can be factorized as
2
×
x
×
x
, and
4
x
can be factorized as
2
×
2
×
x
.
Step 2:
Find the greatest common factor of the two terms. Here, we see that
2
x
is the greatest common factor. We keep this factor outside the brackets, divide the polynomial terms by this factor and write the remaining expression inside the brackets.
Step 3:
Thus, the expression is factorized as
2
x
(
x
+
2
)
Method 2:
Applying Identities
This method involves formulas of algebraic expression for factorization.
Example 1
x
2
+
6
x
+
9
We see that there are no common factors for the three terms in the expression.
However, in the expression, we see that
9
is a perfect square.
In this case, we seek the help of algebraic identities to factorize the expression easily.
This expression looks similar to the identity:
(
a
+
b
)
2
=
a
2
+
2
a
b
+
b
2
Comparing the given expression to the identity, we get
a
=
x
,
b
=
3
Therefore, the factors are
(
x
+
3
)
2
or
(
x
+
3
)
(
x
+
3
)
List of Identities to Factorize Algebraic Expressions
Listed below are the formulas of algebraic expressions.
(
a
+
b
)
2
=
a
2
+
2
a
b
+
b
2
(
a
−
b
)
2
=
a
2
−
2
a
b
+
b
2
a
2
−
b
2
=
(
a
+
b
)
(
a
−
b
)
a
3
+
b
3
=
(
a
+
b
)
(
a
2
−
a
b
+
b
2
)
a
3
−
b
3
=
(
a
−
b
)
(
a
2
+
a
b
+
b
2
)
(
a
+
b
)
3
=
a
3
+
3
a
2
b
+
3
a
b
2
+
b
3
(
a
−
b
)
3
=
a
3
−
3
a
2
b
+
3
a
b
2
−
b
3