# RS Aggarwal Solutions Class 7 Maths Chapter 6 Ex 6.3 (Updated For 2021-22)

RS Aggarwal Solutions Class 7 Maths Chapter 6 Ex 6.3: Want to prepare for your Class 7 Maths exam without any hassle? Try starting your exam prep with RS Aggarwal Solutions Class 7 Maths. It is easy to understand the solutions of RS Aggarwal Solutions Class 7 Maths Chapter 6 Ex 6.3 because of the accuarte and well-explained solutions designed by the subject matter experts.

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RS Aggarwal Solutions Class 7 Maths Chapter 6 Ex 6.3

## RS Aggarwal Solutions Class 7 Maths Chapter 6 Ex 6.3 – Overview

In this exercise, you will solve the problems related to the multiplication operation between the binomial and the monomial.

It can be done via associative property or distributive property. In contrast to this, when we multiply the binomial with another binomial, it also requires the use of the same rules. All of this can be done using the shortcut method of the FOIL i.e., ( First, Out, Inner, Last).

### Multiplying Monomials

A Monomial can be multiplied with another monomial correctly utilizing the properties of the exponents and the properties of the rational numbers.

Let’s say we have to multiply the two monomials i.e., 2x and 5x. It can be multiplied with others using the commutative & associative multiplication properties. It can be done like:

2x × 5x = ( 2 × 5 ) × ( x × x )
2x × 5x = ( 10 ) × (x²)
2x × 5x = 10x²

### Multiplying a Monomial by a Binomial

Multiplying a monomial with a binomial is done using the distributive property rule. Let us take the binomial like 3x + 5 and multiply it further the monomial 2x.

(3x + 5) × 2x = 3x (2x) + 5 (2x)
(3x + 5) × 2x = 6x² + 10x

### Multiplying Two Binomials

While multiplying two binomials, we use the distributive property two times.

Eg: ( x + 2 ) and ( x + 5 ), here, it can be solved via using the distributive property as mentioned below.
( x + 2 ) × ( x + 5 ) = x ( x + 5 ) + 2 ( x + 5 )
( x + 2 ) × ( x + 5 ) = x² + 5x + 2x + 10
( x + 2 ) × ( x + 5 ) = x² + 7x + 10

### Using FOIL Method (First, Out, Inner, Last)

This is the shortcut method that can easily replace the multiplication operation done between monomials and binomials via distribution property.

• Initially multiply the first number contained in each of the binomials, the outside number contained in each of the binomials, the inside number contained in each of the binomials, and the last number contained in each of the binomial” – this is how we perform the calculation via the FOIL method.
• Accumulate all the like numbers, this is to be done by performing the addition operation between the outside terms. This way the result that will see is exactly going to be the same as the distributive property method.
Here, calculating the ( 3x² – 4) ( x – 3 ) by using the FOIL method:

The first number ( 3x² ) ( x ) or 3x³, the outside terms are ( 3x² ) ( -3 ) or -9x², the inside terms ( -4 )( x ) or -4x, and the last numbers are ( -4 ) ( -3 ) which is 12.

Therefore, the expression,
(3x² – 4) (x – 3 ) will be equivalent to the 3x³ – 9x² – 4x + 12

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### How to multiply a monomial with a binomial?

Multiplying a monomial with a binomial is done using the distributive property rule. Let us take the binomial like 3x + 5 and multiply it further the monomial 2x.
(3x + 5) × 2x = 3x (2x) + 5 (2x)
(3x + 5) × 2x = 6x² + 10x

### How to multiply a binomial?

While multiplying two binomials, we use the distributive property two times.
Eg: ( x + 2 ) and ( x + 5 ), here, it can be solved via using the distributive property as mentioned below.
( x + 2 ) × ( x + 5 ) = x ( x + 5 ) + 2 ( x + 5 )
( x + 2 ) × ( x + 5 ) = x² + 5x + 2x + 10
( x + 2 ) × ( x + 5 ) = x² + 7x + 10