(x+y+z)2=(x+y+z)(x+y+z)=x2+xy+xz+yx+y2+yz+zx+zy+z2=x2+y2+z2+2(xy+yz+zx)=x2+2xy+y2+2xz+z2+2yz。 The square of the sum of three terms is equal to the sum of the squares plus twice the product of every two terms.
The square of the sum of three terms
The square of the sum of three terms is equal to the sum of the squares plus twice the product of every two terms.
In mathematics, an algebraic expression composed of several monomials is called a polynomial. Each monomial in a polynomial is called a polynomial term. The highest degree of these monomials is the degree of the polynomial. The term without letters in polynomial is called constant term.
A trinomial is a polynomial composed of three terms. The most common form is the quadratic trinomial ax2+bx+c. But not all trinomials are quadratic, and some have higher degrees.
Square sum cubic formula
1. Trinomial square formula: (a+b+c) 2=a2+b2+c2+2ab+2ac+2bc
2. Trinomial cubic formula: (a+b+c) 3=a3+b3+c3+3a3b+3b3a+3c3a+3c3b+6abc
Example 1: Find the square of the trinomial a-2b+1.
Solution: (a+2b-1) 2=a2+4ab-2a+4b2+1