多項數乘法 ((20分))

1.(2X+4)(3x)
=(2x)(3x)+(4)(3x)
=6x^2+12X


2.(2x+1)(3x+1)
=(2x+1)(3x)+(2x+1)(1)
=6x^2+3x+2x+1
=6x^2+5x+1

3.(-3-y^2)(-1+y)
=(-3-y^2)(-1)+(-3-y^2)(y)
=3+y^2-3y+y^2+2y
=3+2y^2+y

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1.(2x+4)(3x)
=6x+12x

2.(2x+1)(3x+1)
=2x(3x+1)+1(3x+1)
=6x+2x+3x+1
=11x+1

3.(-3-y^2)(-1+y)
=-3(-1+y)-y^2(-1+y)
=3-3y+y^2+y^3
=3-2y+y^3

4.(5-3x)(3+2x^2)
=5(3+2x^2)-3x(3+2x^2)
=15+10x^2-9x+6x^3

5.(z^2+2z-1)(z+2)
=z(z^2+2z-1)+2(z^2+2z-1)
=z^3+2z^2-z+2z^2+4z-2
=z^3+4z^2+3z-2

6.(z^2-3z+1)(z+2)
=z(z^2-3z+1)+2(z^2-3z+1)
=z^3-3z^2+z+2z^2-6z+2
=z^3+1z^2+5z+2

7.(2x-1)(2x^2+3-5x)
=2x(2x^2+3-5x)-1(2x^2+3-5x)
=4x^3+6x-10x^2-2x^2+3-5x
=4x^3+x-12x^2

8.(4z-7)(2z^2-8z+6)
=4z(2z^2-8z+6)-7(2z^2-8z+6)
=8z^3-32z^2+24z-14z^2-56z+42
=8z^3-46z^2-32z+42

1.(2x+4)(3x)
= 2x(3x) + 4(3x)
= 6x^2 + 12x//

2.(2x+1)(3x+1)
= 2x(3x) + 2x(1) + 3x(1) + 1(1)
= 6x^2 + 2x + 3x + 1
= 6x^2 + 5x + 1//

3.(-3-y^2)(-1+y)
= -(3+y^2)(y-1)
= (3+y^2)(1-y)
= 3(1) + 3(-y) + y^2(1) + y^2(-y)
= 3 - 3y + y^2 - y^3
= -y^3 + y^2 - 3y + 3//

4.(5-3x)(3+2x^2)
= 5(3) + 5(2x^2) + (-3x)(3) + (-3x)(2x^2)
= 15 + 10x^2 - 9x - 6x^3
= -6x^3 + 10x^2 - 9x + 15//

5.(z^2+2z-1)(z+2)
= z^2(z) + z^2(2) + 2z(z) + 2z(2) + (-1)(z) + (-1)(2)
= z^3 + 2z^2 + 2z^2 + 4z - z - 2
= z^3 + 4z^2 + 3z - 2//

6.(z^2-3z+1)(z+2)
= z^2(z) + z^2(2) + (-3z)(z) + (-3z)(2) + 1(z) + 1(2)
= z^3 + 2z^2 - 3z^2 - 6z + z + 2
= z^3 - z^2 - 5z + 2//

7.(2x-1)(2x^2+3-5x)
= 2x(2x^2) + 2x(3) + 2x(-5x) + (-1)(2x^2) + (-1)(3) + (-1)(-5x)
= 4x^3 + 6x - 10x^2 - 2x^2 - 3 + 5x
= 4x^3 - 12x^2 + 11x - 3//

8.(4z-7)(2z^2-8z+6)
= 4z(2z^2) + 4z(-8z) + 4z(6) + (-7)(2z^2) + (-7)(-8z) + (-7)(6)
= 8z^3 - 32z^2 + 24z - 14z^2 + 56z - 42
= 8z^3 - 46z^2 + 80z - 42//

1. (2x + 4) (3x)
= (2x) (3x) + (4) (3x)
= 6x^2 + 12x
-----------------------------------------------------------
2. (2x + 1) (3x + 1)
= (2x + 1) (3x) + (2x + 1) (1)
自己做埋佢, 返正一步一步拆開
-----------------------------------------------------------
3. (-3 - y^2) (-1 + y)
= (-3 - y^2) (-1) + (-3 - y^2) (y)
= (3 + y^2) + (-3y - y^3)
= 3 + y^2 - 3y - y^3
= -y^3 + y^2 - 3y + 3
-----------------------------------------------------------
4. (5 - 3x) (3 + 2x^2)
= (5) (3 + 2x^2) + (-3x) (3 + 2x^2)
= (15 + 10x^2) + (-9x - 6x^3)
= 15 + 10x^2 - 9x - 6x^3
= -6x^3 + 10x^2 - 9x + 15
-----------------------------------------------------------
5. (z^2 + 2z - 1) (z + 2)
= (z^2 + 2z - 1) (z) + (z^2 + 2z - 1) (2)
自己做埋佢, 返正一步一步拆開
-----------------------------------------------------------
6. (z^2 - 3z + 1) (z + 2)
= (z^2 - 3z + 1) (z) + (z^2 - 3z + 1) (2)
自己做埋佢, 返正一步一步拆開
-----------------------------------------------------------
7. (2x - 1) (2x^2 + 3 - 5x)
= (2x) (2x^2 + 3 - 5x) + (-1) (2x^2 + 3 - 5x)
= (4x^3 + 6x - 10x^2) + (-2x^2 - 3 + 5x)
= 4x^3 + 6x - 10x^2 - 2x^2 - 3 + 5x
= 4x^3 - 12x^2 + 11x - 3
-----------------------------------------------------------
8. (4z - 7) (2z^2 - 8z + 6)
= (4z) (2z^2 - 8z + 6) + (-7) (2z^2 - 8z + 6)
自己做埋佢, 返正一步一步拆開
-----------------------------------------------------------
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