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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.
(i) y − z
(ii) 
(iii) z2
(iv) 
(v) x2 + y2
(vi) 5 + 3 (mn)
(vii) 10 − yz
(viii) ab − (a + b)
(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 + 7x2 y (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 + 2x2 y2 (e) pq + q (f) 1.2 ab – 2.4 b + 3.6 a (g) 3 4 x + 1 4 (h) 0.1 p2 + 0.2 q2
(i)
(a)
(b)
(c)
(d)
(e)
(ii)
. 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 q – 4pq2 (viii) 7mn (ix) z2 – 3z + 8 (x) a2 + b2 (xi) z2 + z (xii) 1 + x + x2
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
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) 4m2 p, 4mp2 (vi) 12xz, 12x2 z2
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
Identify like terms in the following: (a) – xy2 , – 4yx2 , 8x2 , 2xy2 , 7y, – 11x2 , – 100x, – 11yx, 20x2 y, – 6x2 , y, 2xy, 3x (b) 10pq, 7p, 8q, – p2 q2 , – 7qp, – 100q, – 23, 12q2 p2 , – 5p2 , 41, 2405p, 78qp, 13p2 q, qp2 , 701p
(a) −xy2, 2xy2
−4yx2, 20x2y
8x2, −11x2, −6x2
7y, y
−100x, 3x
−11xy, 2xy
(b) 10pq, −7qp, 78qp
7p, 2405p
8q, −100q
−p2q2, 12p2q2
−23, 41
−5p2, 701p2
13p2q, qp2
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) – p2 q2 + 7pq (vi) 1.2 a + 0.8 b (vii) 3.14 r2 (viii) 2 (l + b) (ix) 0.1 y + 0.01 y2
|
Row |
Expression |
Terms |
Coefficients |
|
(i) |
5 − 3t2 |
− 3t2 |
− 3 |
|
(ii) |
1 + t + t2 + t3 |
t t2 t3 |
1 1 1 |
|
(iii) |
x + 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) |
0.1y + 0.01y2 |
0.1y 0.01y2 |
0.1 0.01 |
(a) Identify terms which contain x and give the coefficient of x. (i) y2 x + y (ii) 13y2 – 8yx (iii) x + y + 2 (iv) 5 + z + 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) 2x2 y – 15xy2 + 7y2
|
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 + x + xy |
x xy |
1 y |
|
(vi) |
12xy2 + 25 |
12xy2 |
12y2 |
|
(vii) |
7x+ xy2 |
7x |
7 |
(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 |
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