Factorisation Of Algebraic Expression

Factorization of algebraic expressions involves finding two or more expressions that multiply together to give the original expression. It's like reversing multiplication. This process helps simplify and understand complex algebraic formulas. We'll also cover common algebraic identities that aid in this factorization process.

Introduction to Factors and Algebraic Expressions

Factors are numbers or quantities that, when multiplied together, produce a given number or expression. For example, the factors of 12 include 1, 2, 3, 4, 6, and 12.

In terms of prime factors, 12 can be expressed as 2² × 3¹.

Similarly, algebraic expressions involve variables, constants, and operators. They consist of terms separated by addition or subtraction. For instance, the expression 3xyz - 16x² - yz has three terms: 3xyz, -16x², and -yz.

Also Check: Factoring Polynomials

Algebraic Expressions Method

Factoring algebraic expressions involves several common methods. These methods include:

  1. Factorization using common faces: Identifying and factoring out the highest common factors from terms in the expression.
  2. Factorization by regrouping terms: Rearranging and regrouping terms within the expression to facilitate factoring.
  3. Factorization using identities: Applying algebraic identities to simplify and factorize expressions.

Factorization using common faces

To factorize an algebraic expression, we reverse the process of expanding it. This involves identifying common factors among terms and grouping them accordingly.

For example, consider the expression -3y2 + 18y:

We can factor out -3y: -3y2 + 18y = -3y(y - 6).

In this way, factoring simplifies and breaks down complex expressions into simpler components.

Also Check: Factors of 215

Factorization by regrouping terms

Factorization by regrouping terms involves rearranging algebraic expressions to identify common factors among the terms. For instance, consider the expression 12a + n - na - 12. Although not all terms share a common factor initially, we can regroup them based on shared factors:

The terms can be rearranged as shown:
12a + n - na - 12 = 12a - 12 + n - na
12a - 12 + n - an = 12(a - 1) - n(a - 1)
12a - 12 + n - an = (12 - n)(a - 1)
We can simplify algebraic expressions by grouping terms.

Also Check: Factors of 144

Factoring Expression using Standard identities

An identity in math is an equality that holds true for all values of variables. For instance:
(a + b)2 = a2 + 2ab + b2
(a - b)2 = a2 - 2ab + b2
a2 - b2 = (a - b)(a + b)

These equations, known as identities, remain valid regardless of the values substituted for a and b.

Factorization of algebraic expressions is a key concept covered in Chapter 14 on factorization. We previously studied factorization of numbers, and now we explore how to factorize algebraic expressions into products of their factors.

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Frequently Asked Questions on Factorisation Of Algebraic Expression

To factorise an algebraic expression, look for a common factor in all the terms. Take out this factor and put it in front of brackets containing the remaining parts of each term.

The key trick in factorization is to identify the greatest common factor (GCF) of all the terms. Once you find the GCF, divide each term by it and put the GCF outside brackets containing the remaining parts.

There is no single formula for factorization. The process involves breaking down an expression into simpler factors. Common methods include taking out a common factor, grouping terms, and using identities like difference of squares.

Algebraic factoring does not have a single formula. It is a process of breaking down an expression into simpler factors. The most common formulas used are:
(a + b)2 = a2 + 2ab + b2
(a - b)2 = a2 - 2ab + b2
a2 - b2 = (a + b)(a - b)

The main methods for factorizing algebraic expressions are:

  1. Taking out a common factor
  2. Grouping terms to find a common factor
  3. Using standard identities like difference of squares or perfect squares.