1. Knowledge background: Paulia said: "In order to get an equation, we must express the same quantity in two different ways, that is, calculate a quantity twice, thus establishing an equal relationship." This is the principle of two calculations. The characteristics of quadratic calculation principle: consider an appropriate quantity from two aspects.
On the one hand, on the other hand, we can get ………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………… Application 1: The usual column equation is actually a kind of "secondary calculation".
Two aspects consider the same quantity, so the results are equal, resulting in an equation (equation), such as the proof of combinatorial identities. Application 2: Equal product method commonly used in geometry.
2. Examples of practical application: (Taiyuan in 2020) Some identities can be obtained by calculating the area of geometric figures. The identity written according to the rectangular area is 2a (a+b) = 2a2+2ab. Analysis: On the one hand, the rectangular area is twice as wide as the length, that is, 2a (a+b).
On the other hand, the area of a rectangle is the sum of the areas of several figures, that is, 2a2+2ab, and 2a (a+b) = 2a2+2ab can be obtained by synthesis. (1) Use the square difference formula verified by the graph to observe the following figure. From figure 1 to figure 2, it can be expressed as (a) a. ..
(A+B) (A-B) = A2-B2B。 A2-B2 =(A+B)(A-B)c .(A+B)2 = A2+2AB+B2D。 A2+2AB+B2 = (A+B) 2 (II) Verifying the complete square with graphs.
1. Using the equivalence relation of areas in the graph, some mathematical formulas can be obtained. For example, according to Figure A, we can get the square formula of the sum of two numbers: (m+n) 2 = m2+2mn+n.
2. According to Figure B, the mathematical formula you can get is (c) a.m2-N2 = (m-n) 2b. (m+n) 2 = m2+2mn+n2c。 (m-n)2 = m2-2mn+n2d . m2-N2 =(m+n)(m-n)。
2. (Monthly Examination of No.37 Middle School in Taiyuan City in 2020) Map 1 is a rectangle with a length of A and a width of B, and now it is spliced into a shape with several equal rectangles.