Solution: [(a-2b)? -2(a-b)(a-2b)]> 2a

=(a-2b)[a-2 b-2(a-b)]\2a

=(a-2b)(a-2b-2a+2b)÷2a

=(a-2b)×(-a)÷2a

=(a-2b)×(- 1/2)

=(4-2× 1)×(- 1/2)

=2×(- 1/2)

=- 1

Interpretation of the meaning of the question:

The method of simplifying polynomials is factorizing polynomials.

Factorization has the following methods:

(1) common factor extraction method:

Such as: am+bm+cm=m(a+b+c)

The method of extracting the common factor is the method of extracting the common factor contained in each item in the polynomial.

For example, this problem is solved by extracting the common factor, (a-2b)? There are two monomials in -2(a-b)(a-2b), namely (a-2b)? And 2(a-b)(a-2b), and the common factor contained in these two monomials is a-2b, then (a-2b) is obtained by extracting the common factor? -2(a-b)(a-2b)=(a-2b)[a-2 b-2(a-b)]=(a-2b)×(-a).

(2) Cross multiplication: The method of cross multiplication is simply: the multiplication on the left of the cross is equal to the quadratic term coefficient, the multiplication on the right is equal to the constant term, and the cross multiplication and addition is equal to the linear term coefficient. In fact, it is to use the multiplication formula (x+a)(x+b)=x? +(a+b)x+ab for factorization.

For example:

Answer? x？ +ax-42

First, let's look at the first number. Is it an a? , representing the multiplication of two A, inferring (ax+? )×(ax+？ ),

Then let's look at the second item. Formula +ax is the result of merging similar terms, so it is inferred as binomial × binomial.

The last term is -42, and -42 is -6×7 or 6×7, which can also be decomposed into -2 1×2 or 2/kloc-0 /× 2.

First of all, 2 1 and 2, whether positive or negative, can't be 1 after any addition or subtraction, but only-19 or 19, so the latter is excluded.

Then, determine whether it is -7×6 or 7×6.

(ax-7)×(ax+6)=a？ x？ -ax-42

The result is inconsistent with the original result, and the original formula +ax becomes -ax.

Recalculate:

(ax+7)×(ax+(-6))=a？ x？ +ax-42

Correct, so a? x？ +ax-42 is decomposed into (ax+7)×(ax-6), which is the popular factorization.

(3) Formula method: factorization is carried out by using some commonly used formulas.

Square difference formula: a? -B? =(a+b)(a-b)

Complete sum of squares formula: a? +2ab+b？ =(a+b)？

Complete square difference formula: a? -2ab+b？ =(a-b)？

Cubic sum formula: a? +b？ =(a+b)(a？ -ab+b？ )

Cubic difference formula: a? -B? =(a-b)(a？ +ab+b？ )

Complete cubic formula: (a b)? =a？ 3a？ b+3ab？ b？ =(a b)？

(4) Equation solving method:

Factorization is achieved by solving equations, such as:

X2+2X+ 1=0, and the original formula =(X+ 1)×(X+ 1) is obtained.