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NCERT solution class 7 chapter 12 Algebraic expressions 12.1 mathematics

EXERCISE 12.1


Page No 234:

Question 1:

Get the algebraicexpressions 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 and b subtracted from their product.

Answer:

(i) y − z

(ii) 

(iii) z2

(iv) 

(v) x2 + y2

(vi) 5 + 3 (mn)

(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 + x2 (c) − y3

(d)  (e) − ab + 2b2 − 3a2

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

(a) − 4x + 5 (b) − 4x + 5y (c) 5+ 3y2

(d)  (e) pq + q

(f) 1.2 ab − 2.4 b + 3.6 (g) 

(h) 0.1p2 + 0.2 q2

Answer:

(i)

(a)

(b)

(c)

(d)

(e)

(ii)

Row

Expression

Terms

Factors

(a)

− 4x + 5

− 4x

5

− 4, x

5

(b)

− 4x + 5y

− 4x

5y

− 4, x

5, y

(c)

5y + 3y2

5y

3y2

5, y

3, yy

(d)

xy + 2x2y2

xy

2x2y2

xy

2, xxyy

(e)

pq q

pq

q

pq

q

(f)

1.2ab − 2.4b + 3.6a

1.2ab

− 2.4b

3.6a

1.2, ab

− 2.4, b

3.6, a

(g)

(h)

0.1p2 + 0.2q2

0.1p2

0.2q2

0.1, pp

0.2, qq

Page No 235:

Question 3:

Identify the numerical coefficients of terms (other than constants) in the following expressions:

(i) 5 − 3t2 (ii) 1 + t2 + t3 (iii) x + 2xy+ 3y

(iv) 100m + 1000n (v) − p2q2 + 7pq (vi) 1.2a + 0.8b

(vii) 3.14 r2 (viii) 2 (b) (ix) 0.1y + 0.01 y2

Answer:

Row

Expression

Terms

Coefficients

(i)

5 − 3t2

− 3t2

− 3

(ii)

1 + t + t2 + t3

t

t2

t3

1

1

1

(iii)

+ 2xy + 3y

x

2xy

3y

1

2

3

(iv)

100m + 1000n

100m

1000n

100

1000

(v)

− p2q2 + 7pq

− p2q2

7pq

− 1

7

(vi)

1.2a +0.8b

1.2a

0.8b

1.2

0.8

(vii)

3.14 r2

3.14 r2

3.14

(viii)

2(l + b)

2l

2b

2

2

(ix)

0.1+ 0.01y2

0.1y

0.01y2

0.1

0.01

Question 4:

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

(i) y2x + y (ii) 13y2− 8yx (iii) x + y + 2

(iv) 5 + zx (v) 1 + x+ xy (vi) 12xy2 + 25

(vii) 7x + xy2

(b) Identify terms which contain y2 and give the coefficient of y2.

(i) 8 − xy2 (ii) 5y2 + 7x (iii) 2x2y −15xy2 + 7y2

Answer:

(a)

Row

Expression

Terms with x

Coefficient of x

(i)

y2x + y

y2x

y2

(ii)

13y2 − 8yx

− 8yx

−8y

(iii)

x + y + 2

x

1

(iv)

5 + z + zx

zx

z

(v)

1 + xy

x

xy

1

y

(vi)

12xy2 + 25

12xy2

12y2

(vii)

7xxy2

7x

xy2

7

y2

(b)

Row

Expression

Terms with y2

Coefficient of y2

(i)

8 − xy2

xy2

− x

(ii)

5y2 + 7x

5y2

5

(iii)

2x2y + 7y2

−15xy2

7y2

−15xy2

7

−15x

Question 5:

Classify into monomials, binomials and trinomials.

(i) 4y − 7z (ii) y2 (iii) x + y − xy

(iv) 100 (v) ab − a − b (vi) 5 − 3t

(vii) 4p2− 4pq2 (viii) 7mn (ix) z2 − 3z + 8

(x) a2 + b2 (xi) z2 + z (xii) 1 + x + x2

Answer:

The monomials, binomials, and trinomials have 1, 2, and 3 unlike terms in it respectively.

(i) 4y − 7z

Binomial

(ii) y2

Monomial

(iii) x + y − xy

Trinomial

(iv) 100

Monomial

(v) ab − a − b

Trinomial

(vi) 5 − 3t

Binomial

(vii) 4p2q − 4pq2

Binomial

(viii) 7mn

Monomial

(ix) z2 − 3z + 8

Trinomial

(x) a2 + b2

Binomial

(xi) z2 + z

Binomial

(xii) 1 + x + x2

Trinomial

Question 6:

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

(i) 1, 100 (ii)  (iii) − 29x, − 29y

(iv) 14xy, 42yx (v) 4m2p, 4mp2 (vi) 12xz, 12 x2z2

Answer:

The terms which have the same algebraic factors are called like terms. However, when the terms have different algebraic factors, these are called unlike terms.

(i) 1, 100

Like

(ii) − 7x

Like

(iii) −29x, −29y

Unlike

(iv) 14xy, 42yx

Like

(v) 4m2p, 4mp2

Unlike

(vi) 12xz, 12x2z2

Unlike

Question 7:

Identify like terms in the following:

(a) −xy2, − 4yx2, 8x2, 2xy2, 7y, − 11x2, − 100x, −11yx, 20x2y, −6x2y, 2xy,3x

(b) 10pq, 7p, 8q, − p2q2, − 7qp, − 100q, − 23, 12q2p2, − 5p2, 41, 2405p, 78qp, 13p2qqp2, 701p2

Answer:

(a) −xy2, 2xy2

−4yx2, 20x2y

8x2, −11x2, −6x2

7yy

−100x, 3x

−11xy, 2xy

(b) 10pq, −7qp, 78qp

7p, 2405p

8q, −100q

p2q2, 12p2q2

−23, 41

−5p2, 701p2

13p2qqp2

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