Algebraic Expressions
Exercise 12.1
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 numbers 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) Subtraction of z from y.
Ans: y – z
(ii) One-half of the sum of numbers x and y.
Ans: ½(x + y)
(iii) The number z multiplied by itself.
Ans: z X z
(iv) One-fourth of the product of numbers p and q.
Ans: ¼ pq
(v) Numbers x and y both squared and added.
Ans: x2 + y2
(vi) Number 5 added to three times the product of numbers m and n.
Ans: 5 + 3mn
(vii) Product of numbers y and z subtracted from 10.
Ans: 10 – yz
(viii) Sum of numbers a and b subtracted from their product.
Ans: ab – (a + b)
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) y – y3
(d) 5xy2 + 7x2y (e) – ab + 2b2 – 3a2
(ii) Identify terms and factors in the expressions given below:
(a) – 4x + 5 (b) – 4x + 5y (c) 5y + 3y2
(d) xy + 2x2y2 (e) pq + q (f) 1.2ab – 2.4b + 3.6a
(g)3/4x +1/4 (h) 0.1 p2 + 0.2 q2
Solution:
(a) – 4x + 5
Terms: – 4x, 5
Factors: (– 4, x) (5)
(b) – 4x + 5y
Terms: – 4x, 5y
Factors: (– 4, x) (5, y)
(c) 5y + 3y2
Terms: 5y , 3y2
Factors: (5, y), (3, y, y )
(d) xy + 2x2y2
Terms: xy , 2x2y2
Factors: (x,y) (2, x, x, y, y)
(e) pq + q
Terms: pq , q
Factors: (p, q) ( q )
(f) 1.2ab – 2.4b + 3.6a
Terms: 1.2ab, – 2.4b , 3.6a
Factors: (1.2, a, b) ( – 2.4, b ) (3.6, a)
(g) 3/4 x + 1/4
Terms: 3/4 x , 1/4
Factors: (3/4 , x ) (1/4)
(h) 0.1p2 + 0.2q2
Terms: 0.1p2, 0.2q2
Factors: (0.1, p, p ) ( 0.2, q, q)
3). Identify the numerical coefficients of terms (other than constants) in the following expressions:
(i) 5 – 3t2 (ii) 1 + t + t2 + t3 (iii) x + 2xy + 3y
(iv) 100m + 1000n (v) – p2q2 + 7pq (vi) 1.2 a + 0.8 b
(vii) 3.14 r2 (viii) 2 (l + b) (ix) 0.1 y + 0.01 y2
Solution:
(i) 5 – 3t2
Term: – 3t2
The coefficient of – 3t2 is – 3
(ii) 1 + t + t2 + t3
Terms: t , t2 , t3
The coefficient of t is 1
The coefficient of t2 is 1
The coefficient of t3 is 1
(iii) x + 2xy + 3y
Terms: x , 2xy , 3y
The coefficient of x is 1
The coefficient of 2xy is 2
The coefficient of 3y is 3
(iv) 100m + 1000n
Terms: 100m , 1000n
The coefficient of 100m is 100
The coefficient of 1000n is 1000
(v) – p2q2 + 7pq
Terms: – p2q2 , 7pq
The coefficient of – p2q2 is – 1
The coefficient of 7pq is 7
(vi) 1.2a + 0.8b
Terms: 1.2a , 0.8b
The coefficient of 1.2a x is 1.2
The coefficient of 0.8b is 0.8
(vii) 3.14 r2
Terms: 3.14 r2
The coefficient of 3.14 r2 is 3.14
(viii) 2 (l + b)
2 (l + b) = 2l + 2b
Terms: 2l , 2b
The coefficient of 2l is 2
The coefficient of 2b is 2
(ix) 0.1y + 0.01y2
Terms: 0.1y , 0.01y2
The coefficient of 0.1y is 0.1
The coefficient of 0.01y2is 0.01
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 + z + zx (v) 1 + x + xy (vi) 12xy2 + 25
(vii) 7x + xy2
Solution:
(i) y2x + y
Terms containing x: y2x
coefficient of x is y2
(ii) 13y2 – 8yx
Terms containing x: – 8yx
coefficient of x is – 8y
(iii) x + y + 2
Terms containing x: x
coefficient of x is 1
(iv) 5 + z + zx
Terms containing x: zx
coefficient of x is z
(v) 1 + x + xy
Terms containing x: x, xy
coefficient of x is 1
coefficient of x is y
(vi) 12xy2 + 25
Terms containing x: 12xy2
coefficient of x is 12y2
(vii) 7x + xy2
Terms containing x: 7x, xy2
coefficient of x is 7
coefficient of x is y2
(b) Identify terms which contain y2 and give the coefficient of y2.
(i) 8 – xy2 (ii) 5y2 + 7x (iii) 2x2y – 15xy2 + 7y2
Solution:
(i) 8 – xy2
Terms containing y2: – xy2
coefficient of y2 is – x
(ii) 5y2 + 7x
Terms containing y2: 5y2
coefficient of y2 is 5
(iii) 2x2y – 15xy2 + 7y2
Terms containing y2: – 15xy2, 7y2
coefficient of y2 is – 15x
coefficient of y2 is 7
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) 4p2q – 4pq2 (viii) 7mn
(ix) z2 – 3z + 8 (x) a2 + b2 (xi) z2 + z (xii) 1 + x + x2
Solution:
(i) 4y – 7z
Ans: It is binomial
(ii) y2
Ans: It is monomial
(iii) x + y – xy
Ans: It is trinomial
(iv) 100
Ans: It is monomial
(v) ab – a – b
Ans: It is trinomial
(vi) 5 – 3t
Ans: It is binomial
(vii) 4p2q – 4pq2
Ans: It is binomial
(viii) 7mn
Ans: It is monomial
(ix) z2 – 3z + 8
Ans: It is trinomial
(x) a2 + b2
Ans: It is binomial
(xi) z2 + z
Ans: It is binomial
(xii) 1 + x + x2
Ans: It is trinomial
6). State whether a given pair of terms is of like or unlike terms.
(i) 1, 100 (ii) –7x, 5/2 x (iii) – 29x, – 29y
(iv) 14xy, 42yx (v) 4m2p, 4mp2 (vi) 12xz, 12x2z2
Solution:
(i) 1, 100
Ans: They are like terms
(ii) –7x, 5/2 x
Ans: They are like terms
(iii) – 29x, – 29y
Ans: They are unlike terms
(iv) 14xy, 42yx
Ans: They are like terms
(v) 4m2p, 4mp2
Ans: They are unlike terms
(vi) 12xz, 12x2z2
Ans: They are unlike terms
7). Identify like terms in the following:
(a) – xy2, – 4yx2, 8x2, 2xy2, 7y, – 11x2, – 100x, – 11yx, 20x2y,
– 6x2, y, 2xy, 3x
Ans: (– xy2, 2xy2 ); ( – 4yx2, 20x2y ); ( 8x2, – 11x2, – 6x2); ( 7y, y );
( – 100x, 3x ); ( – 11yx, 2xy )
(b) 10pq, 7p, 8q, – p2q2, – 7qp, – 100q, – 23, 12q2p2, – 5p2, 41, 2405p, 78qp, 13p2q, qp2, 701p2
Ans: (10pq, – 7qp, 78qp ); (7p, 2405p); (8q, – 100q ); (– 23, 41);
( – p2q2, 12q2p2 ); ( – 5p2, 701p2); ( 13p2q, qp2 )
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