Expressions which present the work of numbers, variables and their degrees are called monomials. The sum of monomials forms a polynomial. Similar composed in a polynomial have the same alphabetic part and can differ in coefficients. To bring similar composed - means to simplify expression.
Instruction
1. Before bringing similar composed in a polynomial, often there is a need to make intermediate actions: to remove all brackets, announce in degree and to bring into a standard look composed. That is to write down them in the form of the work of a numerical multiplier and degrees of variables. For example, expression 3xy (-1.5) y², brought to a standard look, will look so: – 4.5xy³.
2. Remove all brackets. Lower brackets in A+B+C expressions. If brackets are faced by the sign "plus", then signs of all composed remain. If brackets are faced by the sign "minus", then signs all composed change for opposite. For example, (x³–2x) – (11x²–5ax) =x³–2x–11x²+5ax.
3. If at removal of brackets it is required to increase a monomial C by A+B polynomial, apply the distributive law of multiplication (a+b) c=ac+bc. For example, – 6xy(5y–2x) = – 30xy²+12x²y.
4. If it is necessary to increase a polynomial by a polynomial, multiply everything composed among themselves and put the received monomials. At construction of a polynomial of A+B in degree apply formulas of abridged multiplication. For example, (2ax–3y) (4y+5a) =2ax∙4y–3y∙4y+2ax∙5a–3y∙5a.
5. Lead monomials to a standard look. For this purpose group numerical multipliers and degrees with the identical bases. Further multiply them among themselves. If it is required, build a monomial in degree. For example, 2ax∙5a–3y∙5a+(2xa)³=10a²x–15ay+8a³x³.
6. Find in expression composed which have the same alphabetic part. Allocate them with special underlining for descriptive reasons: one direct line, one wavy line, two simple hyphens and so forth.
7. Put coefficients of similar composed. Increase the received number by alphabetic expression. Similar composed are given. For example, x²–2x–3x+6+x²+6x–5x–30–2x²+14x–26=x²+x²–2x²–2x–3x+6x–5x+14x+6–30–26=10x–50.