Mathematics
Factorise the following:
50x2 - 2(x - 2)2
Factorisation
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Answer
50x2 - 2(x - 2)2
= 2[25x2 - (x - 2)2]
= 2[(5x)2 - (x - 2)2].
Using identity,
a2 - b2 = (a - b)(a + b).
2[(5x)2 - (x - 2)2] = 2[5x - (x - 2)][5x + (x - 2)]
= 2(5x - x + 2)(5x + x - 2)
= 2(4x + 2)(6x - 2)
= 2[2(2x + 1)2(3x - 1)]
= 8(2x + 1)(3x - 1).
Hence, 50x2 - 2(x - 2)2 = 8(2x + 1)(3x - 1).
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