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.

Q 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 + x^{2}

(C) y – y^{3} (D) 5xy^{2} + 7x^{2}y

(E) – ab + 2b^{2} – 3a^{2}

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

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) 100 m + 1000 n

(v) –p^{2}q^{2} + 7pq

(vi) 1.2a + 0.8b

(vii) 3.14 r^{2}

(viii) 2(l + b)

(ix) 0.1y + 0.01y^{2}

Q 4.

(A) Identify terms which contains x and give the coefficient of x.

(i) y^{2}x + y (ii) 13y^{2} – 8xy

(iii) x + y + 2 (iv) 5 + z + zx

(v) 1 + x + xy (vi) 12xy^{2} + 25

(vii) 7x + xy^{2}

(B) Identify terms which contains y^{2} and give the coefficient of y^{2}.

(i) 8 – xy^{2} (ii) 5y^{2} + 7x

(iii) 2x^{2}y – 15xy^{2} + 7y^{2}

Q 5.

Classify into monomials, binomials and trinomials.

(i) 4y – 7z (ii) y^{2}

(iii) x + y – xy (iv) 100

(v) ab – a – b (vi) 5 –3t

(vii) 4p^{2}q –4pq^{2} (viii) 7mn

(ix) z^{2} – 3z + 8 (x) a^{2} + b^{2}

(xi) z^{2} + z (xii) 1 + x + x^{2}

Q 6.

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

(i) 1, 100 (ii) −7x,5/2x,

(iii) –29x, – 29y (iv) 14xy, 42yx

(v) 4m^{2}p, 4mp^{2} (vi) 12xz, 12x^{2}z^{2}

Q 7.

Identify like terms in the following:

(A) –xy^{2}, –4yx^{2}, 8x^{2}, 2xy^{2}, 7y, –11x^{2}, –100x, –11yx, 20x^{2}y, –6x^{2}, y, 2xy, 3x

(B) 10pq, 7p, 8q, –p^{2}q^{2}, –7qp, – 100q, –23, 12q^{2}p^{2}, – 5p^{2}, 41, 2405p, 78qp, 13p^{2}q, qp^{2}, 701p^{2}

Q 8.

Simplify by combining like terms:

(i) 21b – 32 + 7b –20b

(ii) –z^{2} + 13z^{2} –5z + 7z^{2} – 15z

(iii) p – (p – q) –q –(q – p)

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

(v) 5x^{2}y – 5x^{2} + 3yx^{2} –3y^{2} + x^{2} – y^{2} + 8xy^{2} – 3y^{2}

(vi) (3y^{2} + 5y – 4) – (8y – y^{2} – 4)

Q 9.

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) 4x^{2}y, –3xy^{2}, –5xy^{2}, 5x^{2}y

(viii)3p^{2}q^{2} – 4pq + 5, –10p^{2}q^{2}, 15 + 9pq + 7p^{2}q^{2}

(ix) ab – 4a, 4b – ab, 4a – 4b

(x) x^{2} – y^{2} – 1, y^{2} – 1 – x^{2}, 1 – x^{2} – y^{2}

Q 10.

Subtract :

(i) –5y^{2} from y^{2}

(ii) 6xy from –12xy

(iii) (a – b) from (a + b)

(iv) a(b – 5) from b (5 – a)

(v) – m^{2} + 5mn from 4m^{2} – 3mn + 8

(vi) – x^{2} + 10x – 5 from 5x – 10

(vii) 5a^{2} –7ab + 5b^{2} from 3ab – 2a^{2} – 2b^{2}

(viii) 4pq – 5q^{2} – 3p^{2} from 5p^{2} + 3q^{2} – pq

Q 11.

(A) What should be added to x^{2} + xy + y^{2} to obtain 2x^{2} + 3xy?

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

Q 12.

What should be taken away from 3x^{2} – 4y^{2} + 5xy + 20 to obtain – x^{2} – y^{2} + 6xy + 20 ?

Q 13.

(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 + 2x^{2}, subtract the sum of 3x^{2} – 5x and –x^{2} + 2x + 5.

Q 14.

If m = 2, find the value of:

(i) m – 2 (ii) 3m – 5

(iii) 9 – 5m (iv) 3m^{2} – 2m – 7

(v) (5m/2)-4

Q 15.

If p = –2, find the value of:

(i) 4p + 7 (ii) –3p^{2} + 4p + 7

(iii) –2p^{3} – 3p^{2} + 4p + 7

Q 16.

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

(i) 2x – 7 (ii) –x + 2

(iii) x^{2} + 2x + 1 (iv) 2x^{2} –x – 2

Q 17.

If a = 2, b = –2, then find the value of:

(i) a^{2} + b^{2} (ii) a^{2} + ab + b^{2}

(iii) a^{2} – b^{2}

Q 18.

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

(i) 2a + 2b (ii) 2a^{2} + b^{2} + 1

(iii) 2a^{2}b + 2ab^{2} + ab (iv) a^{2} + ab + 2

Q 19.

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

Q 20.

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

Q 21.

(i) If z = 10, find the value of z^{3} – 3(z – 10).

(ii) If p = –10, find the value of p^{2} – 2p –100.

Q 22.

What should be the value of a if the value of 2x^{2} + x – a equals to 5, when x = 0?

Q 23.

Simplify the expression 2(a^{2} + ab) + 3 – ab and find its value when a = 5 and b = –3.

Q 24.

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.

Q 25.

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