中一功課..代數式

7A：(x+2)(x-3)
=x^2+2x-3x-6
=x^2-x-6

7b：(3-y)(y+2)
= -y^2+3y-2y+6
= -y^2-y+6

7c：(a-3)(2a-7)
=2a^2-6a-7a+21
=2a^2-13a+21

8a：(4b-5)(2-b)
= -4b^2+8b+5b-10
= -4b^2+13b-10

8b：(2r-4)(4r-3)
=8r^2-16r-6r+12
=8r^2-22r+12

8c：(2w+3)(5-3w)
= -6w^2+5w-15w+15
= -6w^2-10w+15

10a：(x-3)(y+7)
=xy-3y+7x-21

10b：(6+a)(b-2)
=ab-2a+6b-12

10c：(p+q)(r+3)
=pr+qr+3p+3q

11a：(3y-2x)(6x+5y)
=18xy-10xy+15y^2-12x^2
=8XY+15y^2-12x^2

11b：(4x-3y)(7x-2y)
=28x^2+6y^2-21xy-8xy
=28x^2+6y^2-29xy

11c：(5m-6n)(5m-n)
=25m^2+6n^2-30mn-5mn
=25m^2+6n^2-35mn

P.S.^2係2次方

7A:(x+2)(x-3)
=x(x+2)-3(x+2)
=X^2+2x-3x-6
=x^2-x-6
7b:(3-y)(y+2)
=y(3-y)+2(3-y)
=3y-y^2+6-2y
=3y-2y-y^2+6
=y-y^2+6
=-y^2+y+6
7c:(a-3)(2a-7)
=2a(a-3)-7(a-3)
=2a^2-6a-7a+21
=2a^2-13a+21
8a:(4b-5)(2-b)
=2(4b-5)-b(4b-5)
=8b-10-4b^2+5b
=8b+5b-4b^2-10
=10b-4b^2-10
=-4b^2+10b-10
8b:(2r-4)(4r-3)
=4r(2r-4)-3(2r-4)
=8r^2-16r-6r+12
=8r^2-22r+12
8c:(2w+3)(5-3w)
=5(2w+3)-3w(2w+3)
=10w+15-6w^2-9w
=10w-9w-6w^2+15
=w-6w^2+15
=-6w^2+w+15
10a:(x-3)(y+7)
=y(x-3)+7(x-3)
=yx-3y+7x-21
10b:(6+a)(b-2)
=b(6+a)-2(6+a)
=6b+ab-12-2a
10c:(p+q)(r+3)
=r(p+q)+3(p+q)
=pr+qr+3p+3q
11a:(3y-2x)(6x+5y)
=6x(3y-2x)+5y(3y-2x)
=18xy-12x^2+18y^2-10xy
=18xy-10xy-12x^2+18y^2
=8xy-12x^2+18y^2
11b:(4x-3y)(7x-2y)
=7x(4x-3y)-2y(4x-3y)
=28x^2-21xy-8xy+6y^2
=28x^2-29xy+6y^2
11c:(5m-6n)(5m-n)
=5m(5m-6n)-n(5m-6n)
=25m^2-30mn-5mn+6n^2
=25m^2-35mn+6n^2
=25m^2+6n^2-35mn

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7a. x^2 - x - 6
7b. 6 + y - y^2
7c. 2a^2 - 13a + 21

8a. 13b - 4b^2 - 10
8b. 8r^2 -22r + 12
8c. w - w^2 - 15

10a. xy + 7x - 3y - 21
10b. ab - 2a + 6b - 12
10c. pr + 3q + qr + 3q

11a. 15y^2 + 8xy - 12x^2
11b. 28x^2 - 29xy + 6y^2
11c. 25m^2 -35mn + 6n^2