x^2+9xy+18y^2 factorise
Answers
For a polynomial of the form
a
x
2
+
b
x
+
c
, rewrite the middle term as a sum of two terms whose product is
a
⋅
c
=
1
⋅
18
=
18
and whose sum is
b
=
9
.
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Reorder terms.
x
2
+
18
y
2
+
9
x
y
Reorder
18
y
2
and
9
x
y
.
x
2
+
9
x
y
+
18
y
2
Factor
9
out of
9
x
y
.
x
2
+
9
(
x
y
)
+
18
y
2
Rewrite
9
as
3
plus
6
x
2
+
(
3
+
6
)
(
x
y
)
+
18
y
2
Apply the distributive property.
x
2
+
3
(
x
y
)
+
6
(
x
y
)
+
18
y
2
Remove unnecessary parentheses.
x
2
+
3
x
y
+
6
(
x
y
)
+
18
y
2
Remove unnecessary parentheses.
x
2
+
3
x
y
+
6
x
y
+
18
y
2
Factor out the greatest common factor from each group.
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Group the first two terms and the last two terms.
(
x
2
+
3
x
y
)
+
6
x
y
+
18
y
2
Factor out the greatest common factor (GCF) from each group.
x
(
x
+
3
y
)
+
6
y
(
x
+
3
y
)
Factor the polynomial by factoring out the greatest common factor,
x
+
3
y
.
(
x
+
3
y
)
(
x
+
6
y
)
Step-by-step explanation:
x^2+9xy+18y^2
x^2 + (6+3)yx + 18y^2
x^2 + 6xy+3xy + 18y^2
x(x+6y) + 3y(x+6y)
(x+3y)(x+6y)