Mathematics
Factorise:
32a2x3 - 8b2x3 - 4a2y3 + b2y3
Factorisation
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Answer
Given,
⇒ 32a2x3 - 8b2x3 - 4a2y3 + b2y3
⇒ 8x3(4a2 - b2) - y3(4a2 - b2)
⇒ (8x3 - y3)(4a2 - b2)
⇒ (4a2 - b2)[(2x)3 - (y)3]
By using the identity,
(a3 - b3) = (a - b)(a2 + ab + b2)
⇒ (4a2 - b2){(2x - y)[(2x)2 + 2x × y + (y)2]}
⇒ [(2a)2 - (b)2][(2x - y)(4x2 + 2xy + y2)]
By using the identity,
(a2 - b2) = (a + b)(a - b)
⇒ [(2a)2 - (b)2] [(2x - y)(4x2 + 2xy + y2)]
⇒ (2a + b)(2a - b)(2x - y)(4x2 + 2xy + y2).
Hence, 32a2x3 - 8b2x3 - 4a2y3 + b2y3 = (2a + b)(2a - b)(2x - y)(4x2 + 2xy + y2).
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