F.1 Maths(20點!)

1 化簡下列多項式
(a) 7x+5y-4x+3y
=3x+8y
(j) -6a^2+(5ab-3a^2b)-6a^2+(5ab-3a^2b
=-6a^2+5ab-3a^2b-6a^2+5ab-3a^2b
=-6a^2-6a^2+5ab+5ab-3a^2b-3a^2b
=-12a^2+10ab-6a^2b
(l) (7x^2+5x-3)+8x^2-7x+5)
=7x^2+5x-3+8x^2-7x+5
=7x^2+8x^2+5x-7x-3+5
=15x^2-2x+2
(r) 12x^2y+3xy^2-4x^2+2xy^2
=12x^2y+3xy^2+2xy^2-4x^2
=12x^2y+5xy^2-4x^2
(s) 7ab+8a^2b-4ab+3a^2b
=7ab-4ab+8a^2b+3a^2b
=3ab+11a^2b
(t) 7x^2y^3+4x^3y^7-4x^2y^3
=7x^2y^3-4x^2y^3+4x^3y^7
=3x^2y^3+4x^3y^7
(u)6x^2y-2x^3y
=6x^2y-2x^3y
.`.將同類項相加（或相減），異項不能相加（或相減）；
例： a + 2a = 3a 消括號時，若括號前為＋，則括號內的符號不變；
例： (2a+3x)+(4a-x)=2a+3x+4a-x=6a+2x消括號時，若括號前為－，則括號內的＋變為－，－變為＋。
例：(2a+3x)-(4a-x)=2a+3x-4a+x=-2a+4x 2 展開下列多項式
(d) 6x(x^2+5x-3)
=6x^3+30x^2-18x
(h) 3a(a^2b+2bc)
=6abc+3a^(2+2b)
(l) -(x^2-2x+1)(2x)
=-(2x^3-4x^2+2x)
=-2x^3+4x^2-2x


.`.把兩個多項式相乘時，第一個多項式的每一個項都要與第二個多項式的每一個項相乘。
例:(x+2)(2x-5)=2x^2+4x-5x-10=2x^2-x-10
在括號前為-時,首先展開括號內的多項式
例:-(3a+2b)(2a)=-[(3a+2b)(2a)]=-(4a^2+4ab)=-4a^2-4ab

1 化簡下列多項式
(a) 7x+5y-4x+3y
answer: 3x+8y

(j) -6a^2+(5ab-3a^2b)-6a^2+(5ab-3a^2b
answer: -12a^2+10ab-6a^2b = 2(-6a^2+5ab-3a^2b)

(l) (7x^2+5x-3)+8x^2-7x+5)
answer: 15x^2-2x+2

(r) 12x^2y+3xy^2-4x^2+2xy^2
answer: 12x^2y-4x^2+5xy^2

(s) 7ab+8a^2b-4ab+3a^2b
answer: 3ab+11a^2b

(t) 7x^2y^3+4x^3y^7-4x^2y^3
answer: 3x^2y^3+4x^3y^7

(u)6x^2y-2x^3y
answer: 2x^2y(3-x)

有d題目只有開/關括號,唔知原本係點...
化簡第一part多項式只係將同group既攏埋一齊做加減(同group既意思係:x同x既就一齊做加減;y同y既做加減;x^2y就只係同留x^2y做加減;xy^2同x^2y唔同,又要分另一group做)
如果括號前面係"+"號,就直接唔要左個括號就可以,裡面既野都唔駛轉;如果括號前面係"-"號,就只需要將括號入面既符號轉左佢就得(即"+"變"-"及"-"變"+")

2 展開下列多項式
(d) 6x(x^2+5x-3)
answer: 6x^3+30x^2-18x
只要將6x分別乘入"x^2","+5x"及"-3"便可

(h) 3a(a^2b+2bc)
answer: 3a^3b+6abc
同樣,將3a分別乘入"a^2b"及"+2bc"便可

(l) -(x^2-2x+1)(2x)
answer: = - (2x^3-4x^2+2x)
= -2x^3+4x^2-2x
首先,將2x分別乘入"x^2","-"2x"及"+1",再將"-"(即"-1"乘入"2x^3","-4x^2"和"+2x"內),亦即是我所說的「如果括號前面係"-"號,就只需要將括號入面既符號轉左佢就得(即"+"變"-"及"-"變"+")」