Solved Examples on Algebra Formulas
Example 1: Find out the value of the term, (2x + 3)2 using algebraic formulae.
Solution:
Using the algebraic formula,
(a + b)2 = a2 + b2 + 2ab
(2x + 3)2 = (2x)2 + 32 + 2 × 2x × 3
(2x + 3)2 = 4x2 + 9 + 12x
Example 2: Find out the value of the term, (5x – 3y)2 using algebraic formulae.
Solution:
Using the algebraic formula,
(a – b)2 = a2 + b2 – 2ab
(5x – 3y)2 = (5x)2 + (3y)2 – 2 × 5x × 3y
(5 – 3)2 = 25x2 + 9y2 – 30xy
Example 3: Find out the value of, 105×95 using algebraic formulae.
Solution:
Using the algebraic formula,
(a + b)(a – b) = a2 – b2
105×95 = (100+5)(100-5)
= 1002 – 52
= 10000 – 25
= 9975
Example 4: Find the roots of the quadratic equation x2+6x+8=0 using algebra formulas for quadratic equations.
Solution:
Given quadratic equation is x2 + 6x + 8 = 0
Comparing above equation with ax2+bx+c=0, a=1, b=6, c=8
Substituting the values in the quadratic formula we get,
x = [−b ± √(b2 − 4ac)] / 2a
= [−6 ± √(62 − 4(1)(8))] / 2(1)
= [−6 ± √(36 − 4(1)(8))] / 2
= [−6 ± √(36 − 32)] / 2
= [−6 ± √4] / 2
= (-6 + 2) / 2 and (-6 – 2) / 2
= -4/2 and -8/2
= -2 and -4Thus, the values of x are -2 and -4
Algebra Formulas
Algebra Formulas are the basic formulas that are used to simplify algebraic expressions. Algebraic Formulas form the basis for solving various complex problems. Algebraic Formulas help solve algebraic equations, quadratic equations, polynomials, trigonometry equations, probability questions, and others.
An identity is a true equation for any values assigned to the variables. Algebraic Identities are used to solve various equations. For Algebraic Identities, L.H.S is always equal to R.H.S.
Table of Content
- What are Algebra Formulas?
- Algebraic Identities
- Algebra Formulas for Class 8
- Algebra Formulas for Class 9
- Law of Exponent
- Algebra Formulas for Class 10
- Formulas for Arithmetic Sequence
- Formulas for Geometric Sequence
- Algebra Formulas for Class 11
- Algebra Formulas for Class 12
- Solved Examples on Algebra Formulas
- Summarizing Algebra Formulas
- Practice Problems on Algebra Formulas