These NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions Ex 12.1 Questions and Answers are prepared by our highly skilled subject experts.

## NCERT Solutions for Class 7 Maths 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 numbers x and y.

(iii) The number z multiplied by itself.

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

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

(vi) Number 5 added to three times the 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.

Answer:

(i) y – z

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

(iii) z^{2}

(iv) \(\frac { 1 }{ 4 }\)pq

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

(vi) 5 + 3mn

(vii) 10 – yz

(viii) ab – (a + b)

Question 2.

(i) Identify the terms and their factors in the following 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

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

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

(e) pq + q

(f) 1.2ab- 2.4 b + 3.6a

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

(h) 0.1p^{2} + 0.2p^{2}

Answer:

(i) (a) x – 3

Terms : x; – 3 Factors x; -3

1 + x + x^{2}

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

Terms = 1; x; x^{2}

Factors = 1; x; x, x (x^{2} )

(c) y-y^{3}

Terms: y; -y^{3}

Factors y;-1,y,y,y

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

Terms: 5xy^{2}; 7x^{2} y

Factors: 5, x, y, y; 7, x, x, y

(e) -ab + 2b^{2} – 3a^{2}

Terms: -ab; 2b^{2}, -3a^{2}

Factors: -1, a, b; 2; b; b; 3, a, a

(ii)

Expression | Terms | Factors |

(a) -4x + 5 | -4x 5 |
-4x and z 5 and y |

(b) – 4x + 5y | -4x 5y |
– 4 and z 5 and y |

(c) 5y + 3y^{2} |
5y 3y ^{2} |
5 and y 3, y and y |

(d) xy + 2x^{2} y^{2} |
Xy 2x ^{2}y^{2} |
x and y 2, x.x, y and y |

(e) pq + q | Pq q |
p and q q |

(f) 1.2ab – 2.4 b + 3.6a | 1.2ab – 2.4 b 3.6a |
1.2, a and b. -2.4 and b 3.6 and a |

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

(h) 0.lp^{2} + 0.2q^{2} |
0.1p^{2}0.2q ^{2} |
0.1, p,p 0.2, q and q |

Question 3.

Identify the numerical coefficients 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) 100m + 1000n

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

(vi) 1.2a + 0.8b

(vii) 3.14r^{2}

(viii) 2(l + b)

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

Answer:

Expression | Terms (other than constant) | Numerical coefficient |

(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 + lOOOn | 100m 1000n |
100 1000 |

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

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

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

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

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

Question 4.

(a) Identify terms which contain x and give the coefficient of x.

(i) y^{2}x + y

(ii) 13y^{2} – 8yx

(iii) x + y + 2

(iv) 5 + z + zx

(iv) 1+x + xy

(vi) 12xy^{2} + 25

(vii) 7x + xy^{2}

(b) Identify terms which contain y^{2} and give the coefficient of y^{2}.

(i) 8-xy^{2}

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

(iii) 2x^{2}y – 15xy^{2} + 7y^{2}

Answer:

Expression | Term containing x | Coefficient of x |

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

(ii) x + y + 2 | – 8yx | – 8y |

(iii) 5 + z + zx | x | l |

(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 | Term containing y^{2} |
Coefficient of y^{2} |

(i) 8 – xy^{2} |
-xy^{2} |
-X |

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

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

Question 5.

Classify into monomials, binomials and trinomials.

(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}

Answer:

(i) 4y – 7z

The expression 4y – 7z is having two unlike terms (4y and – 7z)

∴ It is a binomial.

(ii) y^{2}

The expression y^{2} is having only one term (y^{2})

∴ It is a monomial.

(iii) x + y – xy

The expression x + y – xy is having three terms (x, y and – xy)

∴ It is a trinomial.

(iv) 100

The expression 100 is having only one term (100)

∴ It is a monomial.

(v) ab – a – b.

The expression ab – a – b is having three terms (ab, -a, and -b)

∴ The expression is a trinomial.

(vi) 5 – 3t

The expression 5 – 3t is having two terms (5 and -3t)

∴ It is a binomial expression.

(vii) 4p^{2}q – 4pq^{2}

The expression 4p^{2}q – 4pq^{2} is having

two unlike terms (4p^{2}q and – 4pq^{2})

∴ The expression is a binomial.

(viii) 7mn

The expression 7mn is having only one term (ie 7mn)

∴ The expression is a monomial.

(ix) z^{2}– 3z + 8

The expression z^{2} – 3z + 8 is having three terms (ie z^{2}, – 3z and 8)

∴ The expression is a trinomial.

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

The expression (a^{2} + b^{2}) is having two unlike terms (a^{2} and b^{2})

∴ It is a binomial expression.

(xi) z^{2} + z

The expression z^{2} + z is having two unlike terms (z2 and z)

∴ The expression in binomial.

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

The expression 1 + x + x^{2} is having three terms (1, x and x^{2})

∴ The expression is a trinomial.

Question 6.

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

(i) 1, 100

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

(iii) -29x, -29y

(iv) 14xy, 42yx

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

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

Answer:

(i) 1, 100 is a pair of like terms.

(ii) \(\frac { 5 }{ 2 }\)x is a pair of like terms.

(iii) – 29x, – 29y is a pair of unlike terms.

(iv) 14xy, 4^{2}yx is a pair of like terms.

(v) 4m^{2}p, 4mp^{2} is a pair of unlike terms.

(vi) 12xz; 12x^{2}z^{2} is a pair of unlike terms.

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}, -7pq, -100q, -23, 12q^{2}p^{2}, -5p^{2}, 41, 2405p, 78qp,

13p^{2}q, qp^{2},701p^{2}

Answer:

(a) -xy^{2} and 2xy^{2}, – 4yx^{2} and 20x^{2} y, 8x^{2}, -11x^{2} and – 6x^{2}; 7y and y; lOOx and 3x; -1 lyx and 2xy are like terms.

(b) 10pq, – 7pq and 78qp.

7p and 2405p; 8q and 100q; – p^{2}q^{2} and 12q^{2}p^{2}; – 23 and 41; – 5p^{2} and 701p^{2}; 13p^{2}q and qp^{2} are like terms.