To learn to simplify expressions in mathematics it is just necessary that correctly and quickly to solve problems, various equations. Simplification of expression means reduction of number of actions that facilitates calculations and saves time.
Instruction
1. Learn to calculate degrees with natural indicators. At multiplication of degrees with the identical bases receive degree of number which basis remains the same, and indicators of degrees develop b^m+b^n=b^(m+n). At division of degrees with the identical bases receive degree of number which basis remains the same, and indicators of degrees are subtracted, and b^m divider indicator is subtracted from an indicator of a dividend: b^n=b^(m-n). At construction of degree in degree the degree of number which basis remains the same turns out, and indicators are multiplied (b^m) ^n=b^(mn) At exponentiation of the work of numbers in this degree each multiplier is built. (abc) ^m=a^m*b^m*c^m
2. Display polynomials on multipliers, i.e. present them in the form of the work of several factors – polynomials and monomials. You put the general multiplier outside brackets. Learn basic formulas of abridged multiplication: difference of squares, sum square, difference square, sum of cubes, difference of cubes, cube of the sum and difference. For example, m^8+2*m^4*n^4+n^8=(m^4) ^2+2*m^4*n^4+(n^4) ^2. These formulas are the main in simplification of expressions. Use method of allocation of a full square in a trinomial of a type of ax^2+bx+c.
3. As often as possible reduce fractions. For example, (2*a^2*b) / (a^2*b*c) =2 / (a*c). But you remember that it is possible to reduce only multipliers. If to multiply numerator and a denominator of algebraic fraction by the same number other than zero, then at the same time the value of fraction will not change. It is possible to transform rational expressions in two ways: a chain and on actions. The second way since it is easier to check results of intermediate actions is more preferable.
4. Quite often in expressions it is necessary to take roots. Roots of even degree are taken only from non-negative expressions or numbers. Roots of odd degree are taken from any expressions.