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 2022-2023 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
CBSE NCERT Class 7 Maths Chapter 12 Exercise 12.4 Solution in Hindi and English Medium
|Chapter: 12||Algebraic Expressions|
|Exercise: 12.4||Videos and PDF Solutions|
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).
Class 7 Maths Exercise 12.4 Extra Questions
Multiply 3x by (2x + 5y).
3x X (2x + 5y) = (3x X 2x) + (3x X 5y) [by distributive law]
= (6x² + 15xy).
Multiply 9/2 x² y by (x + 2y)
(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
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
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.
Class 7 Maths Exercise 12.4 Important Questions
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.