Algebraic Expressions

Subtract 24ab – 10b – 18a from 30ab + 12b + 14a.

Collect like terms and simplify the expression:
12m2 – 9m + 5m – 4m2 – 7m + 10

State with reasons, which of the following pairs of terms are of like
terms and which are of unlike terms:
(i) 7x, 12y (ii) 15x, –21x (iii) – 4ab, 7ba (iv) 3xy, 3x
(v) 6xy2, 9x2y (vi) pq2, – 4pq2 (vii) mn2, 10mn

Identify, in the following expressions, terms which are not
constants. Give their numerical coefficients:
xy + 4, 13 – y2, 13 – y + 5y2, 4p2q – 3pq2 + 5

Observe the patterns of digits made from line segments of equal length. You will find such segmented digits on the display of electronic watches or calculators.

(a)

(b)

(c)

If the number of digits formed is taken to be n, the number of segments required to form n digits is given by the algebraic expression appearing on the right of each pattern.

How many segments are required to form 5, 10, 100 digits of the kind -

 ,  , .

Simplify the expression and find its value when a = 5 and b = -3.

2 (a² + ab) + 3 - ab

What should be the value of a if the value of 2x² + x - a equals to 5, when x = 0?

(i) Ifz = 10, find the value of z³ - 3 (z - 10).

(ii) If p = - 10, find the value of p² - 2p - 100

Simplify these expressions and find their values if x = 3, a = - 1, b = - 2.

(i) 3x - 5 - x + 9 (ii) 2 - 8x + 4x + 4

(iii) 3a + 5 - 8a + 1 (iv) 10 - 3b - 4 - 5b

(v) 2a - 2b - 4 - 5 + a

Simplify the expressions and find the value if x is equal to 2

(i) x + 7 + 4 (x - 5) (ii) 3 (x + 2) + 5x - 7

(iii) 6x + 5 (x - 2) (iv) 4 (2x -1) + 3x + 11

When a = 0, b = - 1, find the value of the given expressions:

(i) 2a + 2b (ii) 2a² + b² + 1

(iii) 2a² b + 2ab² + ab (iv) a² + ab + 2

If a = 2, b = - 2, find the value of:

(i) a² + b² (ii) a² + ab + b² (iii) a² - b²

Find the value of the following expressions, when x = - 1:

(i) 2x - 7 (ii) - x + 2 (iii) x² + 2x + 1

(iv) 2x² - x - 2

If p = -2, find the value of:

(i) 4p + 7

(ii) -3p² + 4p + 7

(iii) -2p³ - 3p² + 4p + 7

If m = 2, find the value of:

(i) m - 2 (ii) 3m - 5 (iii) 9 - 5m

(iv) 3m² - 2m - 7 (v) 

(a) From the sum of 3x - y + 11 and - y - 11, subtract 3x - y - 11.

(b) From the sum of 4 + 3x and 5 - 4x + 2x², subtract the sum of 3x² - 5x and
- x² + 2x + 5.

What should be taken away from 3x² - 4y² + 5xy + 20 to obtain

- x² - y² + 6xy + 20?

(a) What should be added to x² + xy + y² to obtain 2x² + 3xy?

(b) What should be subtracted from 2a + 8b + 10 to get - 3a + 7b + 16?

Subtract:

(i) - 5y² from y²

(ii) 6xy from - 12xy

(iii) (a - b) from (a + b)

(iv) a (b - 5) from b (5 - a)

(v) - m² + 5mn from 4m² - 3mn + 8

(vi) - x² + 10x - 5 from 5x - 10

(vii) 5a² - 7ab + 5b² from 3ab - 2a² -2b²

(viii) 4pq - 5q² - 3p² from 5p² + 3q² - pq

(i) 3mn, - 5mn, 8mn, -4mn

(ii) t - 8tz, 3tz - z, z - t

(iii) - 7mn + 5, 12mn + 2, 9mn - 8, - 2mn - 3

(iv) a + b - 3, b - a + 3, a - b + 3

(v) 14x + 10y - 12xy - 13, 18 - 7x - 10y + 8xy, 4xy

(vi) 5m - 7n, 3n - 4m + 2, 2m - 3mn - 5

(vii) 4x²y, - 3xy², - 5xy², 5x²y

(viii) 3p²q² - 4pq + 5, - 10p²q², 15 + 9pq + 7p²q²

(ix) ab - 4a, 4b - ab, 4a - 4b

(x) x² - y² - 1 , y² - 1 - x², 1- x² - y²

Simplify combining like terms:

(i) 21b - 32 + 7b - 20b

(ii) - z² + 13z² - 5z + 7z³ - 15z

(iii) p - (p - q) - q - (q - p)

(iv) 3a - 2b - ab - (a - b + ab) + 3ab + b - a

(v) 5x²y - 5x² + 3y x² - 3y² + x² - y² + 8xy² -3y²

(vi) (3 y² + 5y - 4) - (8y - y² - 4)

Identify like terms in the following:

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

(b) 10pq, 7p, 8q, - p²q², - 7qp, - 100q, - 23, 12q²p², - 5p², 41, 2405p, 78qp, 13p²q, qp², 701p²

(i) 1, 100 (ii)   (iii) - 29x, - 29y

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

(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

(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

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

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

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) 1.2a + 0.8b

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

(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)  

 (e) - ab + 2b² - 3a²

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

(a) - 4x + 5 (b) - 4x + 5y (c) 5y + 3y²

(d)  

 (e) pq + q

(f) 1.2 ab - 2.4 b + 3.6 a (g) 

(h) 0.1p² + 0.2 q²

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 a and b subtracted from their product.