(vii) x²{x4-(32_z2)2} + y2 (74-Cz2-x2)2} + z{{z4-(x2-y2)2} + (x2+y2–z2)(y2+z2-x2)(z2+x2-y2) = 4x2y2z2 prove this.
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Answer:
Apply the formula a
2
−b
2
=(a+b)(a−b) to simplify the expression.
(x
2
+y
2
−z
2
)
2
−(x
2
−y
2
+z
2
)
2
=(x
2
+y
2
−z
2
+x
2
−y
2
+z
2
){x
2
+y
2
−z
2
−(x
2
−y
2
+z
2
)}
=(2x
2
)(x
2
+y
2
−z
2
−x
2
+y
2
−z
2
)
=(2x
2
)(2y
2
−2z
2
)
=(4x
2
)(y
2
−z
2
)
=4x
2
y
2
−4x
2
z
2
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