Haryana State Board HBSE 7th Class Maths Solutions Chapter 12 Algebraic Expressions Ex 12.1 Textbook Exercise Questions and Answers.

## Haryana Board 7th Class Maths Solutions Chapter 12 Algebraic Expressions Exercise 12.1

Question 1.

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

(i) Subtraction of z from y.

(ii) One half of the sum of number x and y.

(iii) The number z multiplied by itself.

(iv) One fourth of the product of number p and q.

(v) Number x and y both squared and added.

(vi) Number 5 added to three times and product of number m and n.

(vii) Product of numbers y and z subtracted from 10.

(viii) Sum of numbers a and b subtracted from their product.

Solution:

(i) y -z

(ii) \(\frac{1}{2}\) (x + y)

(iii) z x z =z^{2}

(iv) \(\frac{1}{4}\) (p x q) = \(\frac{1}{4}\) (pq) = \(\frac{pq}{4}\)

(v) x^{2} + y^{2}

(vi) 3mn + 5

(vii) 10 – yz

(viii) ab – (a + b)

Question 2.

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

(a) x – 3

(b) 1 + x + x^{2}

(c) y – y^{3}

(d) 5xy^{2} + 7x^{2}y

(e) -ab + 2b^{2} – 3a^{2}

(ii) Identify terms and factors in the expressions given below:

(a) -4x + 5

(b) -4x + 5y

(e) 5y + 3y^{2}

(d) xy + 2x^{2}y^{2}

(e) pq+q

(f) 1.2ab – 2.4b + 3.6a

(g.) \(\frac{3}{4} x+\frac{1}{4} h\)

(h) \(\frac{l+m}{5}\)

[Hint: Separate l and m terms]

(j) 0.1p^{2} + 0.2q^{2}

(j) \(\frac{3}{4}\) (a – b) + \(\frac{7}{4}\)

[Hint: Open the brackets]

Solution:

(i) (a) x – 3: In this expression x – 3 consists two terms x and -3.

(ii) (a) – 4x + 5.

The expression (- 4x + 5) consists of two terms – 4x and 5. The term – 4x is product of – 4 and x. And the term 5 has only one factor that is 5.

Terms are – 4x and 5.

Factors are-4 andx, of-4x and factor 5 of 5.

(b) -4x + 5y

In the expression -4x + 5y The terms are – 4x and 5y and factors are- 4 and x of-4x and 5 andy of 5y.

(c) 5y + 3y^{2}

In the expression 5y + 3y^{2}

The terms are 5y and 3y^{2} and factors are 5 and y of 5y, 3, y and y of 3y^{2}.

(d) xy + 2x^{2}y^{2}

In the expression xy + 2x^{2}y^{2}

The terms are xy and 2x^{2}y^{2}

And factors are x and y of xy and 2, x, x, y and y of 2x^{2}y^{2}.

(e) pq + q

In the expression pq + q.

The terms are pq and q.

The factors are p and q of pq and q of q because q has only one factor.

(f) In the expression 1.2ab – 2.4b + 3.6a

The terms are 1.2ab, 2.4b and 3.6a and

factors are 1.2, a and b of 1.2ab, 2.4, and 6 of 2.4b; 3.6 and a of 3.6a.

(g) \(\frac{3}{4} x+\frac{1}{4}\)

(i) 0.1p^{2} + 0.2q^{2}

In this expression 0.1 p^{2} + 0.2 q^{2}

The terms are 0.1 p^{2} and 0.2 q^{2} and factors are 0.1, p, p of 0.1 p^{2} and 0.2, q, q of 0.2 q^{2}.

Question 3.

Identify the numerical co¬efficients of terms other than constants in the following expressions:

(i) 5-3t^{2}

(ii) 1 + t + t^{2} + t^{3}

(iii) x + 2xy + 3y

(iv) 100 m + 1000 n

(v) – p^{2}q^{2} + 7pq

(vi) 1.2a + 0.8 b

(vii) 3.14 r^{2}

(viii) 2(l + b)

(ix) 0.1 y + 0.01 y^{2}.

Solution:

Expression | Terms |
Numerical Co-efficient |

(i) 5 – 3t^{2} |
-3t^{2} |
-3 |

(ii) 1 + t + t^{2} + t^{3} |
t t ^{2}t ^{3} |
1 1 1 |

(iii) x + 2xy + 3y | x 2xy 3y |
1 2 3 |

(iv) 100 m + 1000 n | 100 m 1000 n |
100 1000 |

(v) – p^{2}q^{2} + 7pq |
-(p^{2}q^{2})7pq |
-1 7 |

(vi) 1.2a + 0.86 | 1.2a 0.86 |
1.2 0.8 |

(vii) 3.14 r^{2} |
3.14 r^{2} |
3.14 |

(viii) 2(l + b) = 2l + 2b | 2l 2b |
2 2 |

(ix) 0.1y + 0.01 y^{2} |
0.1y 0.01y ^{2} |
0.1 0.01 |

Question 4.

(a) Identify terms which contain x and give the co-efficient of x.

(i) y^{2}x + y

(ii) 13y^{2} – 8yx

(iii) x + y + 2

(iv) 5 + z + zx

(v) 1 + x +xy

(vi) 12xy^{2} + 25

(vii) 7x + xy^{2}

(b) Identify terms which contains y^{2} and give the co-efficient of y^{2}.

(i) 8 – xy^{2}

(ii) 5y^{2} + 7x

(iii) 2x^{2}y – 15xy^{2} + 7y^{2}

Solution:

(a)

Expression | Terms – with factor (x) | Co-efficient of x |

(i) y^{2}x + y |
y^{2}x |
y^{2} |

(ii) 13y^{2} – 8yx |
-8yx | -8y |

(iii) x + y + 2 | x | 1 |

(iv) 5 + z + zx | zx | z |

(v) 1 + x + xy | x xy |
1 y |

(vi) 12xy^{2} + 25 |
12xy^{2} |
12y^{2} |

(vii) 7x + xy^{2} |
7x xy ^{2} |
7 y ^{2} |

(b)

Expression | Terms with factor y^{2} |
Co-efficient of y^{2} |

(i) 8-xy^{2} |
-xy^{2} |
– X |

(ii) 5y^{2} + 7x |
5y^{2} |
5 |

(iii) 2xy^{2} – 15xy^{2} + 7y^{2} |
2xy^{2
}-15xy^{2
}7y^{2} |
2x -15x 7 |

Question 5.

Classify into monomials, binomials and trinomials. Give reasons for your answer:

(i) 4y – 7z

(ii) y^{2}

(iii) x + y – xy

(iv) 100

(v) ab-a-b

(vi) 5 – 3t

(vii) 4p^{2}q – 4pq^{2}

(viii) 7mn

(ix) z^{2} – 3z + 8

(x) a^{2} + b^{2}

(xi) z^{2} + z

(xii) 1 + x + x^{2}

Solution:

(i) 4y – 7z is binomial. It contain 2 terms.

(ii) y^{2} is monomial. It contains 1 term.

(iii) x + y – xy is trinomial.lt contains 3 terms.

(iv) 100 is monomial. It contains 1 term.

(v) ab-a-b is trinomial.lt contains3 terms

(vi) 5 – 3t is binomial. It contains 2 terms.

(vii) 4p^{2}q – 4pq^{2} is binomial.lt contains 2 terms.

(viii) 7mn is monomial. It contains 1 term.

(ix) z^{2} – 3z + 8 is trinomial. It contains 3 terms.

(x) a^{2} + b^{2} is binomial. It contain 2 terms.

(xi) z^{2} + z is binomial. It contains 2 terms.

(xii) 1 + x + x^{2} is trinomial. It contains 3 terms.

Question 6.

State whether the given pair of terms is of like or unlike terms.

(i) 1,100

(ii) -7x, \(\frac{5}{2}\)x

(iii) – 29x, – 29y

(iv) 14xy, 42xy

(v) 4m^{2}p,4mp^{2}

(vi) 12xz, 12x^{2}z^{2}

Solution:

Pairs | Factors |
Like / Unlike Terms |

(i) 1, | 1 | Unlike |

100, | 100 | |

(ii) – 7x | – 7, x | 1 |

5/2 x | 5/2, x | Like |

(iii) -29x | -29, x | |

-29y | – 29, y | Unlike |

(iv) 14 xy | 14, x, y | |

42 yx | 42, x, y | Like |

(v) 4m^{2}p |
4, m, m, p | |

4mp^{2} |
4, m, p, p | Unlike |

(vi) 12xz | 12, x, z | |

12x^{2}z^{2} |
12, x, x, z, z | , Unlike |

Question 7.

Identify like terms in the following:

(a) – xy^{2}, – 4yx^{2}, 8x^{2}, 2xy^{2}, 7y, – 11x^{2}, – 100x, -11yx, 20x^{2}y, -6x^{2}, y, 2xy, 3x.

(b) 10pq, 7p, 8q, – p^{2}q^{2}, – 7qp, – 100q, – 23, 12q^{2}p^{2}, -5P^{2}, 41, 2405p, 78qp, 13p^{2}q, – 9pq^{2}, qp^{2}, 701P^{2}.

Solution: