Last updated on August 5th, 2025
Algebraic formulas are essential in mathematics for solving problems involving variables and constants. They help simplify expressions and solve equations. In this topic, we will explore key algebraic formulas for basic operations, such as addition, subtraction, multiplication, and division.
To work with algebraic expressions, we need formulas for basic operations like addition, subtraction, multiplication, and division. Let’s learn these essential algebraic formulas.
The addition of algebraic expressions involves combining like terms. For example, the addition of two expressions, a + b and c + d, is given by: (a + b) + (c + d) = a + b + c + d
Subtraction in algebra involves taking away one expression from another.
For example, subtracting c + d from a + b is: (a + b) - (c + d) = a + b - c - d
The multiplication of algebraic expressions requires applying the distributive property.
For example, multiplying (a + b) by (c + d) results in: (a + b)(c + d) = ac + ad + bc + bd
Division in algebra involves simplifying expressions.
For example, dividing a + b by c is: (a + b) / c = (a/c) + (b/c)
In mathematics and real life, algebraic formulas simplify complex problems and make calculations easier. They are crucial for:
Students often make errors when working with algebraic formulas. Here are some common mistakes and ways to avoid them.
Simplify (3x + 4) + (5x + 6)?
The simplified expression is 8x + 10
Combine like terms: 3x + 5x = 8x 4 + 6 = 10
So, the expression is 8x + 10
Simplify (7y + 3) - (2y + 5)?
The simplified expression is 5y - 2
Subtract each term: 7y - 2y = 5y 3 - 5 = -2
So, the expression is 5y - 2
Multiply (x + 2) by (x + 3)?
The product is x^2 + 5x + 6
Apply the distributive property:
x(x + 3) + 2(x + 3) = x2 + 3x + 2x + 6
Combine like terms: x2 + 5x + 6
Divide (6z + 12) by 3?
The quotient is 2z + 4
Divide each term by 3: 6z / 3 = 2z 12 / 3 = 4
So, the expression is 2z + 4
Simplify (4a + 5b) - (2a + 3b)?
The simplified expression is 2a + 2b
Subtract each term: 4a - 2a = 2a 5b - 3b = 2b
So, the expression is 2a + 2b
Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.
: He loves to play the quiz with kids through algebra to make kids love it.