Factorise the following: x4-y4+x2-y2
Answers
Answer:
Let us solve x
4
+y
4
+x
2
y
2
=(x
4
+y
4
+2x
2
y
2
)−x
2
y
2
=(x
2
+y
2
)
2
−(xy)
2
Using a
2
−b
2
=(a+b)(a−b)
x
4
+y
4
+x
2
y
2
=(x
2
+y
2
+xy)(x
2
+y
2
−xy)
Hence, option C is correct
Answer:
x
4
−y
4
+x
2
−y
2
</p><p>=(x+y)(x−y)[(x
2
+y
2
+1]
Step-by-step explanation:
\begin{gathered}x^{4}-y^{4}+x^{2}-y^{2}\\=[(x^{2})^{2}-(y^{2})^{2})]+x^{2}-y^{2}\\=(x^{2}+y^{2})(x^{2}-y^{2})+x^{2}-y^{2}\end{gathered}
x
4
−y
4
+x
2
−y
2
=[(x
2
)
2
−(y
2
)
2
)]+x
2
−y
2
=(x
2
+y
2
)(x
2
−y
2
)+x
2
−y
2
\* By algebraic identity :
\boxed {a^{2}-b^{2}=(a+b)(a-b)}
a
2
−b
2
=(a+b)(a−b)
*\
=(x^{2}-y^{2})[(x^{2}+y^{2}+1](x
2
−y
2
)[(x
2
+y
2
+1]
=(x+y)(x-y)[(x^{2}+y^{2}+1](x+y)(x−y)[(x
2
+y
2
+1]
Therefore,
\begin{gathered}x^{4}-y^{4}+x^{2}-y^{2}\\ < /p > < p > =(x+y)(x-y)[(x^{2}+y^{2}+1]\end{gathered}
x
4
−y
4
+x
2
−y
2
</p><p>=(x+y)(x−y)[(x
2
+y
2
+1]
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