J's answer to Olivia tan's Secondary 2 Maths Singapore question.
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(a + b - c)(ab - bc - ca) + abc
= (a + b)(ab - bc - ca) - c(ab - bc - ca) + abc
= (a + b)(ab - bc - ca) - cab + c²b + c²a + abc
= (a + b)(ab - bc - ca) + c²(a + b) - abc + abc
= (a + b)(ab - bc - ca + c²)
= (a + b)(b(a - c) - c(a - c))
= (a + b)(b - c)(a - c)
(xy - 1)(x - 1)(y + 1) - xy
= (xy - 1)(xy + x - y - 1) - xy
= (xy - 1)(xy - 1 + x - y) - xy
= (xy - 1)(xy - 1 + x) - (xy - 1)y - xy
= (xy - 1)(xy - 1 + x) - y(xy - 1 + x)
= (xy - 1 - y)(xy - 1 + x)
= ((x - 1)y - 1)((y + 1)x - 1)
= (a + b)(ab - bc - ca) - c(ab - bc - ca) + abc
= (a + b)(ab - bc - ca) - cab + c²b + c²a + abc
= (a + b)(ab - bc - ca) + c²(a + b) - abc + abc
= (a + b)(ab - bc - ca + c²)
= (a + b)(b(a - c) - c(a - c))
= (a + b)(b - c)(a - c)
(xy - 1)(x - 1)(y + 1) - xy
= (xy - 1)(xy + x - y - 1) - xy
= (xy - 1)(xy - 1 + x - y) - xy
= (xy - 1)(xy - 1 + x) - (xy - 1)y - xy
= (xy - 1)(xy - 1 + x) - y(xy - 1 + x)
= (xy - 1 - y)(xy - 1 + x)
= ((x - 1)y - 1)((y + 1)x - 1)
Date Posted:
3 years ago
Why the down vote? Anything you don't understand?
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