Factorize (i) a⁴ - 6a² - 7 - 8x - x²
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Step-by-step explanation:
a
4
−6a
2
−7−8x−x
2
=(a
2
)
2
−2×a
2
×3+3
2
−3
2
−7−(x
2
+2×x×4+4
2
−4
2
)
=(a
2
)
2
−2×a
2
×3+3
2
)−9−7−(x
2
+2×x×4+4
2
)+16
=(a
2
)
2
−2×a
2
×3+3
2
)−16−(x
2
+2×x×4+4
2
)+16
=(a−3)
2
−(x+4)
2
=[(a−3)+(x+4)][(a−3)−(x+4)]
=(a−3+x+4)(a−3−x−4)
=(a+x+1)(a−x−7)
Therefore.,
\red {a^{4}-6a^{2}-7-8x-x^{2}}\green {= (a+x+1)(a-x-7) }a
4
−6a
2
−7−8x−x
2
=(a+x+1)(a−x−7)
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