The product of lcm and hcf of two numbers is 24 if one of the number is 6 then the other number is

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Standard Eight Mathematics_>Algebra>Exercise 3.7>Q 14

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1. Multiplication of Algebraic Expressions:

When two algebraic expressions are multiplied, the following steps are followed:

(i) Multiply the sign of the terms

(ii) Multiply the corresponding co-efficient of the terms

(iii) Multiply the variable factors by using laws of exponents

2. Types of Products of Algebraic Expressions:

Product of algebraic expressions may be of four different ways:

(i) Product of a monomial with a monomial

(ii) Product of a polynomial with a monomial

(iii) Product of a binomial with a binomial

(iv) Product of a polynomial with a polynomial

3. Types of Division of Algebraic Expressions:

There are four ways of division on algebraic expressions.

(i) Monomial by a Monomial

(ii) Polynomial by a Monomial: For dividing a Polynomial with Monomial, divide each term of the Polynomial by the Monomial.

(iii) Polynomial by a Binomial

(iv) Polynomial by a Polynomial

4. Identity:

An identity is an equation which is satisfied by any value that replaces its variable(s). The common identities are

(i) a+b2=a2+2ab+b2

(ii) a-b2=a2-2ab+b2

(iii) a2-b2=a+ba-b

(iv) x+ax+b=x2+a+bx+ab

(v) a+b3=a3+3a2b+3ab2+b3

(vi) a-b3=a3-3a2b+3ab2-b3

(vii) x+ax+bx+c=x3+a+b+cx2+ab+bc+cax+abc

5. Factorisation:

Expressing an algebraic expression as the product of two or more expressions is called Factorisation.

6. Algebraic Equations:

(i) An equation is a statement that asserts the equality of two expressions; the expressions are written one on each side of an equal to “=” sign.

(ii) An equation containing only one variable with its highest power as one is called a Linear equation in one variable.

(iii) This linear equation in one variable is also known as a Simple equation.

(iv) The value which replaces a variable in an equation to make the two sides of the equation equal is called a Solution or Root of the equation.

(v) The shifting of a number from one side of the equation to other is called Transposition.

7. Cartesian Plane:

(i) The horizontal line in a graph is named XOX’, called the X-axis. The vertical line is named as YOY’, called the Y-axis. Both the axes are called Coordinate axes. The plane containing the X-axis and the Y-axis is known as Cartesian Plane.

(ii) A point is denoted by a pair (a,b) of two numbers ‘a’ and ‘b’ listed in a specific order in which ‘a’ represents the distance along the X-axis and ‘b’ represents the distance along the Y-axis. It is called an ordered pair (a,b).

(iii) The coordinate axes divide the plane of the graph into four regions called Quadrants.

8. Linear Graph:

(i) Graphing is a visual method for showing relationships between numbers.

(ii) The line graph for the linear equation is called a linear graph.

9. Parallel Lines:

(i) If a line is parallel to the X-axis, its distance from the X-axis is the same and it is represented as y=c.

(ii) If a line is parallel to the Y-axis, its distance from the Y-axis is the same and it is represented as x=k. (Here c, k are constants)

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