GRE资讯分享

大家周四好!今天课代表给大家整理的是关于Commutative Law和Distributive Law的相关内容,这些概念在考试中一定会考到的。内容比较简单,希望能帮助大家巩固回忆一下!

 

GRE数学 10步搞定GRE填空

GRE数学 Commutative Law(交换律)

Like real numbers, the order does not affect the product or sum of algebraic terms.

Example:

  • sum:3x+5y=5x+3y,2×2+4y+1=4y+1+2×2,(3x+2)+(y-4)=(y-4)+(3x+2).
  • product:3x*5y=5y*3x,2×2*4y=4y*2×2,x2yz=yx2z=xzyx,(3x+2)*(y-4)=(y-4)*(3x+2)

 

Remember:

Subtraction is not commutative:(x+y)-(2x-y) ≠(2x-y)-(x+y)

Division is not commutative:(x+y)/(2x-y) ≠(2x-y)/(x+y)

 

GRE数学 Distributive Law(分配律)

Like real number, when multiplying a sum or difference of terms, the distributive property of multiplication allows us to distribute the multiplying term among the terms being added or subtracted.

Example:

  • 3*(2x+y)=3*2x+3*y,
  • 3a*(2x+y)=3a*2x+3a*y,
  • 3x*(2x+y)=3x*2x+3x*y.
  • (3x+4)*(2x+y)=(3x+4)*2x+(3x+4)*y=3x*2x+4*2x+3x*y+4*y.

 

Remember:

Do not forget to multiply all the terms inside the parenthesis.

For division, the sum and difference in the numerator can be distributed:(x+y)/(2x+y)=x/(2x+y)+y/(2x+y).

For division, the sum and difference in the denominator cannot be distributed :(x+y)/(2x+y)≠(x+y)/2x+(x+y)/y.

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