factorise a^12x^4-a^4x12^
Answers
Answered by
2
Step-by-step explanation:
Using a
2
−b
2
=(a+b)(a−b) at each step
Given:a
12
x
4
−a
4
x
12
=a
4
x
4
(a
8
−x
8
), factor out common factor a
4
x
4
=a
4
x
4
[(a
4
)
2
−(x
4
)
2
]
=a
4
x
4
(a
4
+x
4
)(a
4
−x
4
)
=a
4
x
4
(a
4
+x
4
)[(a
2
)
2
−(x
2
)
2
]
=x
4
a
4
(a
4
+x
4
)(a
2
+x
2
)(a
2
−x
2
)
=x
4
a
4
(a
4
+x
4
)(a
2
+x
2
)(a+x)(a−x)
Answered by
2
Answer:
Given :-
➪ a¹²x⁴ - a⁴x¹²
Solution :-
➪ a¹²x⁴ - a⁴x¹²
➭ a⁴x⁴(a⁸ - x⁸)
➭ a⁴x⁴{(a⁴)² - (x⁴)²}
➭ a⁴x⁴(a⁴ + x⁴) (a⁴ - x⁴)
➭ a⁴x⁴(a⁴ + x⁴) {(a²)² - (x²)²}
➭ a⁴x⁴(a⁴ + x⁴) (a² + x²) (a² - x²)
➭ a⁴x⁴(a⁴ + x⁴) (a² + x²) {(a)² - (x)²}
➭ a⁴x⁴(a⁴ + x⁴) (a² + x²) (a + x) (a - x)
∴ The value of a¹²x⁴ - a⁴x¹² is
a⁴x⁴(a⁴ + x⁴) (a² + x²) (a + x) (a - x)
Formula used :-
➪ a² - b²
➭ (a + b) (a - b)
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