幾題maths......請幫幫手!!!!(10分!!)

1.Factorize y²-x²+2x-1

y² - x² + 2x - 1

=y² - (x² - 2x + 1)

= y² - (x-1)²

= [y-(x-1)][y-(x+1)] ........... as a²b² = (a-b)(a+b)

= (y-x+1)(y-x-1)

= (-x+y+1)(-x+y-1)

= (x-y-1)(x-y+1)

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2.if Ax²-B(x²-x)≡4X²+10x,find A and B

Ax² - B(x²-x)
= Ax² - Bx² + Bx
= (A-B)x² + Bx

As Ax²-B(x²-x) ≡ 4x²+10x
i.e. (A-B)x² + Bx ≡ 4x²+10x

So the coefficients of x² and x are equal, so

A-B = 4 .......... (1)
B = 10 ............ (2)

Substitute (2) into (1),

A-(10) = 4
A = 14

So A = 14 and B = 10.

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3. Simplify...

(a) xy+xz-y²-yz/ xy-y²

(xy+xz-y²-yz) / (xy-y²)

= [x(y+z) - y(y+z)] / y(x-y)

= (x-y)(y+z) / y(x-y)

= (y+z)/y

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(b)
12 6 5a
--÷-- x---
a b 4b

(12/a) ÷ (6/b) x (5a/4b)

= (12/a) (b/6) (5a/4b)

= [12(b)(5a)] / [a(6)(4b)]

= 60ab / 24ab

= 5/2

1.Factorize y²-x²+2x-1

y² - x² + 2x - 1

=y² - (x² - 2x + 1)

= y² - (x-1)²

= [y+(x-1)][y-(x-1)] ........... as a²b² = (a-b)(a+b) { correction }

= (y+x-1)(y-x+1)