(a+b)^2=a^2+2ab+b^2。 (a-b)^2=a^2-2ab+b^2。 a^2+b^2=(a+b)^2-2aba2+b2=(a-b)^2+2ab。 (a+b)^2-(a-b)^2=4ab。 a^2+b^2+c^2=(a+b+c)^2-2(ab+ac+bc)。
Knowledge expansion:
definition
The square of the sum of two numbers is equal to the sum of their squares plus twice their product. (a+b)？ =a？ ﹢2ab+b？
The square of the difference between two numbers is equal to the sum of their squares minus twice their product. ﹙a-b﹚？ =a？ ﹣2ab+b？
This formula is an important knowledge base for algebraic operation and deformation, and is often used for factorization. The key point of this knowledge point is to remember and apply the complete square formula. The difficulty lies in understanding the characteristics of the formula (such as understanding the coefficient of the first term of the product in the formula).
Structural characteristics of two formulations:
1, the left is the product of two identical binomials, and the right is the trinomial, which is the sum of the squares of two terms in the binomial on the left, plus or minus twice the product of these two terms.
2. When the two symbols on the left are the same, all the symbols on the right are connected with "+"; When the symbols of the two items on the left are opposite, the square items on the right are connected by "+"and then multiplied by "-"twice (note: the symbols of the items are not included here).
3. The letters in the formula can represent specific numbers (positive or negative numbers) or mathematical formulas, such as monomials or polynomials.
Matters needing attention
1, and on the left is the complete square of a binomial.
2. On the right is the sum of binomial squares, plus (or minus) twice the product of these two terms. A and b can be numbers, monomials and polynomials.
Whether it is (a+b)2 or (a-b)2, the last item is a plus sign. Don't take it for granted that the previous symbol is the next symbol.
4. Don't miss the next project.
5. Don't confuse formulas.
6. Don't make mistakes in the symbols in the operation results.
7, variant application is difficult, not easy to master.
8. The most important thing is to do the questions carefully.