Constants, variables, and arithmetic operators, such as 3x – 2, make up an algebraic expression. To make calculations in algebra simpler, variables are substituted with integers. For this, algebraic formulas are employed. Finding one or more numbers that, when used as a substitute for the variables in the equation, produce the identity is the first step in solving an algebraic problem. These figures are referred to as zeroes.
Formulas of Algebraic Expressions
Algebraic expressions can be categorized into various types based on the number of terms and powers of variables. Some of them are given below: Monomial: ax, ax2, x3,… Binomial, ax + b, ax2 + b, ax2 + bx,…. Trinomial: ax2 + bx + c, ax3 + bx2 + cx,…. The basic alegbraic identities are: (p + q)2 = p2 + q2 + 2pq (p – q)2 = p2 + q2 – 2pq (p + q) (p – q) = p2 – q2 There are other algebra formulas too apart from these basic ones. ChatGPT
Algebraic expressions can be classified into different types based on the number of terms and variable powers. Examples include:
- Monomial: ax, ax2, x3, and so on.
- Binomial: ax + b, ax2 + b, ax2 + bx, and so on.
- Trinomial: ax2 + bx + c, ax3 + bx2 + cx, and so on.
In addition to these basic types, there are various other algebraic formulas, including the following fundamental identities:
- (p + q)2 = p2 + q2 + 2pq
- (p – q)2 = p2 + q2 – 2pq
- (p + q) (p – q) = p2 – q2
Determine the numerical result of (3y + 6)2.
(3y + 6)2
By applying the identity (r + s)2 = r2 + s2 + 2rs, where r = 3y and s = 6, we can simplify this expression:
(3y + 6)2 = (3y)2 + 62 + 2 × 3y × 6
= 9y2 + 36 + 36y