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## NCERT Class 7 Maths Textbook Chapter 12 With Answer PDF Free Download

### Chapter 12: Algebraic Expressions

The topics covered in the chapter are as follows.

- How are Expressions Formed
- Terms of An Expression
- Like and Unlike Terms
- Monomials, Binomials, Trinomials and Polynomials
- Addition and Subtraction of Algebraic Expressions
- Finding The Value of An Expression
- Using Algebraic Expressions – Formulas and Rules

#### 12.1 INTRODUCTION

We have already come across simple algebraic expressions like x + 3, y – 5, 4x + 5, 10y – 5, and so on.

In Class VI, we have seen how these expressions are useful in formulating puzzles and problems. We have also seen examples of several expressions in the chapter on simple equations.

Expressions are a central concept in algebra. This Chapter is devoted to algebraic expressions. When you have studied this chapter, you will know how algebraic expressions are formed, how they can be combined, how we can find their values, and how they can be used.

#### 12.2 HOW ARE EXPRESSIONS FORMED?

We now know very well what a variable is. We use letters x, y, l, m, … etc. to denote variables. A variable can take various values. Its value is not fixed. On the other hand, a constant has a fixed value. Examples of constants are 4, 100, –17, etc.

We combine variables and constants to make algebraic expressions. For this, we use the operations of addition, subtraction, multiplication and division.

We have already come across expressions like 4x + 5, 10y – 20. The expression 4x + 5 is obtained from the variable x, first by multiplying x by the constant 4 and then adding the constant 5 to the product.

Similarly, 10y – 20 is obtained by first multiplying y by 10 and then subtracting 20 from the product. The above expressions were obtained by combining variables with constants.

We can also obtain expressions by combining variables with themselves or with other variables.

Author | NCERT |

Language | English |

No. of Pages | 20 |

PDF Size | 1450 KB |

Category | Education |

Source/ Credits | ncert.nic.in |

### NCERT Solutions Class 7 Maths Chapter 12 Algebraic Expressions

**Q1.** Get the algebraic expressions in the following cases using variables, constants, and arithmetic operations.

**Q2. (i)** Identify the terms and their factors in the following expressions. Show the terms and factors by tree diagrams.

**Ex 12.2 Class 7 Maths Question 1.**Simplify combining like terms:

(i) 21b -32 + 7b- 206

(ii) -z

^{2}+ 13z2 -5z + 7z

^{3}– 15

^{2}

(iii) p – (p – q) – q – (q – p)

(iv) 3a – 2b — ab – (a – b + ab) + 3ab + 6 – a

(v) 5x

^{2}y – 5x

^{2}+ 3yx

^{2}– 3y

^{2}+ x

^{2}– y

^{2}+ 8xy

^{2}-3y

^{2}

(vi) (3y

^{2}+ 5y – 4) – (8y – y

^{2}– 4)

Solution:

(i) 21b – 32 + 7b – 206

Re-arranging the like terms, we get

216 + 7b – 206 – 32

= (21 + 7 – 20)b – 32

= 8b – 32 which is required.

(ii) -z^{2} + 13z^{2} – 5z – 15z

Re-arranging the like terms, we get

7z^{3} – z^{2} + 13z^{2} – 5z + 5z – 15z

= 7z^{3} + (-1 + 13)z^{2} + (-5 – 15)z

= 7z^{3} + 12z^{2} – 20z which is required.

**2. Add:**

**(i) 3mn, – 5mn, 8mn, – 4mn**

**Solution:-**

When term have the same algebraic factors, they are like terms.

Then, we have to add the like terms

= 3mn + (-5mn) + 8mn + (- 4mn)

= 3mn – 5mn + 8mn – 4mn

= mn (3 – 5 + 8 – 4)

= mn (11 – 9)

= mn (2)

= 2mn

**(ii) t – 8tz, 3tz – z, z – t**

**Solution:-**

When term have the same algebraic factors, they are like terms.

Then, we have to add the like terms

= t – 8tz + (3tz – z) + (z – t)

= t – 8tz + 3tz – z + z – t

= t – t – 8tz + 3tz – z + z

= t (1 – 1) + tz (- 8 + 3) + z (-1 + 1)

= t (0) + tz (- 5) + z (0)

= – 5tz

**(iii) – 7mn + 5, 12mn + 2, 9mn – 8, – 2mn – 3**

**Solution:-**

When term have the same algebraic factors, they are like terms.

Then, we have to add the like terms

= – 7mn + 5 + 12mn + 2 + (9mn – 8) + (- 2mn – 3)

= – 7mn + 5 + 12mn + 2 + 9mn – 8 – 2mn – 3

= – 7mn + 12mn + 9mn – 2mn + 5 + 2 – 8 – 3

= mn (-7 + 12 + 9 – 2) + (5 + 2 – 8 – 3)

= mn (- 9 + 21) + (7 – 11)

= mn (12) – 4

= 12mn – 4

NCERT Class 7 Maths Textbook Chapter 12 With Answer PDF Free Download