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Byju's Answer
Standard VII
Mathematics
Multiplication of Algebraic Expressions
Find the prod...
Question
Find the product:
(x – y − z) (x
2
+ y
2
+ z
2
+ xy – yz + xz)
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Solution
(x – y − z) (x
2
+ y
2
+ z
2
+ xy – yz + xz)
=
(
x
+
-
y
+
−
z
)
(
x
2
+
y
2
+
z
2
+
x
y
–
y
z
+
x
z
)
We
know
a
+
b
+
c
a
2
+
b
2
+
c
2
-
a
b
-
b
c
-
c
a
=
a
3
+
b
3
+
c
3
-
3
a
b
c
Here
,
a
=
x
,
b
=
-
y
,
c
=
-
z
(
x
+
-
y
+
−
z
)
(
x
2
+
y
2
+
z
2
+
x
y
–
y
z
+
x
z
)
=
x
3
-
y
3
-
z
3
-
3
x
y
z
Suggest Corrections
3
Similar questions
Q.
Find the product
(
x
+
y
−
z
)
(
x
2
+
y
2
+
z
2
−
x
y
+
y
z
+
z
x
)
.
Q.
Find the product using appropriate identity:
(
x
+
y
−
z
)
(
x
2
+
y
2
+
z
2
−
x
y
+
y
z
+
z
x
)
Q.
If
x
2
+
x
y
+
x
z
=
135
,
y
2
+
y
z
+
x
y
=
351
and
z
2
+
x
z
+
y
z
=
243
, then
x
2
+
y
2
+
z
2
=
?
Q.
Using the identity and proof:
x
3
+
y
3
+
z
3
−
3
x
y
z
=
(
x
+
y
+
z
)
(
x
2
+
y
2
+
z
2
−
x
y
−
y
z
−
z
x
)
.
Q.
Find
x
2
+
y
2
+
z
2
if
x
2
+
x
y
+
x
z
=
135
,
y
2
+
y
z
+
y
x
=
351
and
z
2
+
z
x
+
z
y
=
243
.
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