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Show that (x+a+b)(x+a-b)(x-a+b)(x-a-b) simplifies to x^4-2x^2(a^2+b^2)+(a^2-b^2)^2
MATHEMATICS · Subjective · CBSE · Mathematics · Polynomials · Polynomials
Problem
Show that
(
x
+
a
+
b
)
(
x
+
a
−
b
)
(
x
−
a
+
b
)
(
x
−
a
−
b
)
(x+a+b)(x+a-b)(x-a+b)(x-a-b)
(
x
+
a
+
b
)
(
x
+
a
−
b
)
(
x
−
a
+
b
)
(
x
−
a
−
b
)
simplifies to
x
4
−
2
x
2
(
a
2
+
b
2
)
+
(
a
2
−
b
2
)
2
.
x^4-2x^2(a^2+b^2)+(a^2-b^2)^2.
x
4
−
2
x
2
(
a
2
+
b
2
)
+
(
a
2
−
b
2
)
2
.
Present each step of your working clearly, arranging intermediate results in descending powers of
x
x
x
.
Related theory
Algebraic Identities
Polynomials
Polynomial Functions
Algebra
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