Solution of Chapter 12. Algebraic Expressions (NCERT - Mathematics Book)

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 number y and z subtracted from 10.

(viii) Sum of numbers a and b subtracted from their product.

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

Identify terms and factors in the expression 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)

(h) 0.1p² + 0.2q²

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

(i) 5 - 3t²

(ii) 1 + t + t² + t³

(iii) x + 2xy + 3y

(iv) 100m + 100n

(v) -p²q² + 7pq

(vi) 1.2a + 0.8b

(vii) 3.14r²

(viii) 2(l + b)

(ix) 0.1y + 0.01y²

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

Identify terms which contain and give the coefficient of y².

(i) 8 - xy²

(ii) 5y² + 7x

(iii) 2x²y - 15xy² + 7y²

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

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

(i) 1, 100

(ii) -7x,

(iii) -29x, -29y

(iv) 14xy, 42yx

(v) 4m²p, 4mp²

(vi) 12xz, 12x²z²

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

Simplify combining like terms:

(i) 21b - 32 + 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 + 3xy² - 3x² + x² - y² + 8xy² - 3y²

(vi) (3y² + 5y – 4) – (8y - y² – 4)

Add:

(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

Subtract:

(i) -5y² _– from y²

(ii) 6xyfrom -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 x²

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

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

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

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

What should be taken away form 3x² - 4y² + 5xy + 20 to obtain -x² - y² + 6xy + 20?

From the sum of 3x - y + 11 and -y – 11, subtract 3x - y - 11.

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

If m = 2, find the value of :

(i) m – 2

(ii) 3m – 5

(iii) 9 – 5m

(iv) 3m² - 2m - 7

(v)

If p=-2 find the value of:

(i) 4p + 7

(ii) -3p² + 4p + 7

(iii) -2p³ - 3p² + 4p +7

Find the values of the following expressions when x=-1:

(i) 2x - 7

(ii) -x + 2

(iii) x² + 2x +1

(iv) 2x²- x -2

If a = 2, b = - 2, find the value of :

(i) a² + b²

(ii) a² + ab + b²

(iii) a² - b²

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

(i) 2a + 2b

(ii) 2a² + b²+1

(iii) 2a²b + 2ab² + ab

(iv) a² + ab +2

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

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

If z = 10, find the value of z³ – 3(z – 10)

If p = -10, find the value of p² – 2p – 100

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

Simplify the expression and find its value when a=5 and b = -3, then 2(a² + ab) +3 - ab

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

Use the given algebraic expression to complete the table of number patterns.