(x^2 – y^2) (x^2 + y^2) + (y^2 – z^2) (y^2 + z^2) + (z^2 – x^2) (z^2 + x^2) when x = 12 and y = 13......pls find the value of the expression.....pls slove this i will give u brainlist
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Answer:
x(y
2
−z
2
)+y(z
2
−x
2
)+z(x
2
−y
2
)=xy
2
−xz
2
+yz
2
−yx
2
+zx
2
−zy
2
Arrange the terms in descending order of power of x.
=−x
2
y+zx
2
+xy
2
−xz
2
−y
z
+yz
2
=−x
2
(y−z)+x(y
2
−z
2
)−yz(y−z)
=−x
2
(y−z)+x(y−z)(y+z)−yz(y−z)
=(y−z)[−x
2
+x(y+z)−yz]
(y−z)[−x
2
+xy+xz−yz]
Arrange the term in bracket in descending order of the power of y.
=(y−z)[xy−yz−x
2
+xz]
=(y−z)[−y(−x+z)+x(−x+z)]
=(x−y)(y−z)(z−x).
Step-by-step explanation:
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