中一英文數學(展開同簡化) 5一定答曬

潘慧妍

2009-07-26 8:12 am

1. Simplify-2x^2(2x-5)+4x(3x^2+1).

2. Expand (a) (x+y)(x^2-xy=y^2)
(b) (x-y)(x^2+xy+y^2)
(c) (x-y)(x^4+x^3y+x^2y^2+xy^3+y^4)
(d) (a+b+1)(a+b-1) [Hint: consider x=a+b]
(e) (a+b+c+d)(a+b-c-d) [Hint: consider x=a+b and y=c+d]
(c) (x^2+x+1)(x^2-X+1)

3. Correct the following caculations.
(a) (x+y)^2=x^2+y^2
(b) 2×[(2a)×(3b)]
=2×(2a)×2×(3b)

4. What can be multiplied to x- 2 to give a product containing the
term -3x^2? Find the polynomial. [Note: there are more than one
answers.]

回答 (1)

Hamker

2009-07-26 8:50 am

✔ 最佳答案

1.-2x^2(2x-5)+4x(3x^2+1)
=-2x[x(2x-5)-2(3x^2+1)]
=-2x(2x^2-5x-6x^2-2)
=-2x(-4x^2-5x-2)

2a.(x+y)(x^2-xy+y^2)
=x^3-x^2y+xy^2+x^2y-xy^2+y^3
=x^3+y^3
b.(x-y)(x^2+xy+y^2)
=x^3+x^2y+xy^2-x^2y-xy^2-y^3
=x^3-y^3
c.(x-y)(x^4+x^3y+x^2y^2+xy^3+y^4)
=x^5+x^4y+x^3y^2+x^2y^3+xy^4-x^4y-x^3y^2-x^2y^3-xy^4-y^5
=x^5-y^5
d.(a+b+1)(a+b-1)
=(a+b)^2-1
=a^2+2ab+b^2-1
e.(a+b+c+d)(a+b-c-d)
=(a+b+c+d)[a+b-(c+d)]
=(a+b)^2-(c+d)^2
=a^2+2ab+b^2-(c^2+2cd+d^2)
=a^2+2ab+b^2-c^2-2cd-d^2
f.(x^2+x+1)(x^2-X+1)
=(x^2+2x+1-x)(x^2-2x+1+x)
=[(x+1)^2-x][(x-1)^2+x]
=(x^2-1)^2+x(x+1)^2-x(x-1)^2-x^2
=x^4-2x^2+1+x^3+2x^3+x-x^3+2x^2-x-x^2
=x^4+1+2x^3-x^2
=x^4+2x^3-x^2+1

3a.(x+y)^2
=x^2+2xy+y^2
b.2×[(2a)×(3b)]
=2×6ab
=12ab

4.-3x,1.5x^2

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