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新gre数学重要考点：Distributive Law
Distributive Law
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.
新gre数学重要考点：Associative Law
Associative Law
Like real numbers, the grouping does not affect the product or sum of 3 or more algebraic terms.
Example:
Sum:2x2+(4y+1)=(2x2+4y)+1,
3x+(2xy+5y+2)=(3x+2xy)+(5y+2)=(3x+2xy+5y)+2.
Product:3x*(2y*4xy)=(3x*2y)*4xy=3x*2y*4xy.
Remember:
Typically, same variable is grouped together in a single term and the product of same variable is expressed as power.
新gre数学重要考点：Commutative Law
Commutative Law
Like real numbers, the order does not affect the product or sum of algebraic terms.
Example:
sum:3x+5y=5x+3y,2x2+4y+1=4y+1+2x2,(3x+2)+(y-4)=(y-4)+(3x+2).
product:3x*5y=5y*3x,2x2*4y=4y*2x2,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)
新gre数学重要考点：Substitution
Substitution
Substitution is a method where one or more variables in an expression is replaced by numbers or another set of variables.To evaluate an expression specific numbers are used as substitute. To express in terms of another set of variables, variables are replaced by the new set of variables.
Example:
If x=3, then 2x2+4x+1 can be evaluated by substituting 3 for x.
Replacing all x by 3, we get 2*32+4*3+1=31.
If x=2+y, then x2-3 can be expressed in terms of y by replacing all x by (2+y):(2+y)2-3=y2+4y+1.
Remember:
Do not forget to replace all occurrences of the variable.
After substitution the variable does not appear anywhere in the expression.
由于美国数学基础教育的难度增加导致数学考试越来越难，但新gre数学复习考点都是高中时候学到的知识点，考生不要过于紧张，把基本概念弄明白，再记住一些新版gre数学必备的词汇，那么相信新版gre数学应该没有问题。
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