# NCERT Solutions for Class 7 Maths Chapter 12 Exercise 12.4

NCERT Solutions for Class 7 Maths Chapter 12 Exercise 12.4 (Ex. 12.4) Algebraic Expression in PDF file format free to use online or download. All the contents are updated according to latest CBSE Syllabus 2020-2021 based on new NCERT Books.

There are only two questions in exercise 12.4, which are very easy and interesting to do. Question number 1 is practice question which can be learn by doing it practically using the matchsticks.## Class 7 Maths Chapter 12 Exercise 12.4 Solution

Class: 7 | Mathematics |

Chapter: 12 | Algebraic Expressions |

Exercise: 12.4 | Videos and PDF Solutions |

### CBSE NCERT Class 7 Maths Chapter 12 Exercise 12.4 Solution in Hindi and English Medium

### Class 7 Maths Chapter 12 Exercise 12.4 Solution in Videos

#### Multiplication of a Monomial and a Binomial

p x (q + r) = (p x q) + (p x r).

##### Multiply 3x by (2x + 5y).

We have:

3x X (2x + 5y) = (3x X 2x) + (3x X 5y) [by distributive law]

= (6x² + 15xy).

##### Multiply 9/2 x² y by (x + 2y)

We have:

(9/2 x² y) X (x + 2y)

= (9/2 x² y) X x + 2y X (9/2 x² y) [ by distributive law]

= (9/2 X x²⁺¹ y) + (2 X 9/2 X x² y¹⁺¹)

= 9/2 x³ y + 9 x² y²

##### Multiplication of Two Binomials

Suppose (a + b) and (c + d) are two binomials. By using the distributive law of multiplication over addition twice, we may find their product as given below:

(a + b) x (c + d) = a x (c + d) + b x (c + d)

= (a x c + a x d) + (b x c + b x d)

= ac + ad + bc + bd.

This method is the known as the horizontal method.

##### Multiply (3x + 5y) and (5x – 7y)

We have: (3x + 5y) x (5x – 7y) = 3x X (5x – 7y) + 5y X (5x – 7y)

= (3x X 5x – 3x X 7y) + (5y X 5x – 5y X 7y)

= (15x² -21xy) + (25xy – 35y²)

= 15x² -21xy + 25xy – 35y²

= 15x² + 4xy – 35y²

So, (3x + 5y) x (5x – 7y) = 15x² + 4xy – 35y²

##### How do you multiply polynomial expressions?

To multiply two polynomials:

(i) Multiply each term in one polynomial by each term in the other polynomial.

(ii) Add those answers together, and simplify if needed.

##### How are algebraic expressions and polynomials connected?

Polynomials are algebraic expressions that contain any number of terms combined by using addition or subtraction. A term is a number, a variable, or a product of a number and one or more variables with exponents. Like terms (same variable or variables raised to the same power) can be combined to simplify a polynomial.

##### Neha is 5 years younger to Karishma 12 years ago Karishma was twice as old as Neha. Convert it into an algebraic expression (equation).

Let present age of Karishma is x years

Then age of Neha is x – 5 years

12 Years ago the age of Karishma and Neha was

x – 12 and x- 5 – 12 years respectively.

And 12 years ago age of Karishma twice as of Neha

So, x – 12 = 2 X (x- 17)

or, x – 12 = 2 x- 34

Or, x = 22

hence, present age of Karishma is 22 years and Neha 17 years.