Class 7 Algebraic Expressions Ex 10.1

1. Get the algebraic expressions in the following cases using variables, constants and arithmetic operations.

(i) Subtraction of \(z\) from \(y - = y – z\)

(ii) One-half of the sum of numbers \(x\) and \(y = \dfrac{1}{2} (x + y)\) =\(= \dfrac{(x + y)}{2} \)

(iii) The number \(z\) multiplied by itself \(= z × z= z^2)\)

(iv) One-fourth of the product of numbers \(p\) and \(q = \dfrac{ 1}{4}(p × q)\) \(=\dfrac{ pq}{4}\)

(v) Numbers \(x\) and \(y\) both squared and added \(= x^2 + y^2\)

(vi) Number \(5\) added to three times the product of numbers \(m\) and \(n = 3mn + 5\)

(vii) Product of numbers \(y\) and \(z\) subtracted from \(10 = 10 – (y × z) = 10 – yz\)

(viii) Sum of numbers \(a\) and \(b\) subtracted from their product \(= (a × b) – (a + b) = ab – (a + b)\)

2. (i) Identify the terms and their factors in the following expressions

Show the terms and factors by tree diagrams.

(a) \(x – 3\)

Solution:-

Expression: \(x – 3\)

Terms: \(x, -3\)

Factors: \(x; -3\)

(b) \(1 + x + x^2\)

Solution:-

Expression: \(1 + x + x^2\)

Terms: \(1, x, x^2\)

Factors: \(1; x; x,x\)

(c) \(y – y^3\)

Solution:-

Expression: \(y – y^3\)

Terms: \(y, -y^3\)

Factors: \(y; -y, -y, -y\)

(d) \(5xy^2 + 7x^2y\)

Solution:-

Expression: \(5xy^2 + 7x^2y\)

Terms: \(5xy^2, 7x^2y\)

Factors: \(5, x, y, y; 7, x, x, y\)

(e) \(-ab + 2b^2 – 3a^2\)

Solution:-

Expression: \(-ab + 2b^2 – 3a^2\)

Terms: \(-ab, 2b^2, -3a^2\)

Factors: \(-a, b; 2, b, b; -3, a, a\)

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

(a) \(– 4x + 5\) (b) \(– 4x + 5y\) (c) \(5y + 3y^2\) (d) \(xy + 2x^2y^2\) (e) \(pq + q\) (f) \(1.2 ab – 2.4 b + 3.6 a\) (g)\(\dfrac{3}{4} x + \dfrac{1}{4}\) (h) \(0.1 p^2 + 0.2 q^2\)

Solution:-

Expressions is defined as, numbers, symbols and operators (such as +. – , × and ÷) grouped together that show the value of something.

In algebra a term is either a single number or variable, or numbers and variables multiplied together. Terms are separated by + or – signs or sometimes by division.

Factors is defined as, numbers we can multiply together to get another number.

3. 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) \(– p^2q^2 + 7pq\) (vi) \(1.2 a + 0.8 b\) (vii) \(3.14 r^2\) (viii) \(2 (l + b)\)(ix) \(0.1 y + 0.01 y^2\)

Solution:-

4. (a) Identify terms which contain \(x\) and give the coefficient of \(x\).

(i) \(y^2x + y\) (ii) \(13y^2 – 8yx\) (iii) \(x + y + 2\) (iv) \(5 + z + zx\) (v) \(1 + x + xy\) (vi) \(12xy^2 + 25\) (vii) \(7x + xy^2\)

Solution:-

(b) Identify terms which contain \(y^2\) and give the coefficient of \(y^2\).

(i) \(8 – xy^2\) (ii) \(5y^2 + 7x\) (iii) \(2x^2y – 15xy^2 + 7y^2\)

Solution:-

5. Classify into monomials, binomials and trinomials.

(i) \(4y – 7z\)

Solution:-

Binomial.

(ii) \(y^2\)

Solution:-

Monomial.

(iii) \(x + y – xy\)

Solution:-

Trinomial.

(iv) \(100\)

Solution:-

Monomial.

(v) \(ab – a – b\)

Solution:-

Trinomial.

(vi) \(5 – 3t\)

Solution:-

Binomial.

(vii) \(4p^2q – 4pq^2\)

Solution:-

Binomial.

(viii) \(7mn\)

Solution:-

Monomial.

(ix) \(z^2 – 3z + 8\)

Solution:-

Trinomial.

(x) \(a^2 + b^2\)

Solution:-

Binomial.

(xi) \(z^2 + z\)

Solution:-

Binomial.

(xii) \(1 + x + x^2\)

Solution:-

Trinomial.

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

(i) \(1, 100\)

Solution:-

Like term.

(ii) \(–7x, (\dfrac{5}{2})x\)

Solution:-

Like term.

(iii) \(– 29x, – 29y\)

Solution:-

Unlike terms.

(iv) \(14xy, 42yx\)

Solution:-

Like term.

(v) \(4m^2p, 4mp^2\)

Solution:-

Unlike terms.

(vi) \(12xz, 12x^2z^2\)

Solution:-

Unlike terms.7. Identify like terms in the following:

(a) \(– xy^2, – 4yx^2, 8x^2, 2xy^2, 7y, – 11x^2, – 100x, – 11yx, 20x^2y, – 6x^2, y, 2xy, 3x\)

Solution:-

When term have the same algebraic factors, they are like terms.

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

(b) \(10pq, 7p, 8q, – p^2q^2, – 7qp, – 100q, – 23, 12q^2p^2, – 5p^22, 41, 2405p, 78qp, 13p^2q, qp^2, 701p2\)

Solution:-

When term have the same algebraic factors, they are like terms.

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