CBSE Class 7 Mathematics Chapter 12: Algebraic Expressions NCERT Solutions

We can form algebraic expressions by using variables, constants, and the four basic arithmetic operations. Here's how each case is represented:

1. (i) The expression for 'subtraction of z from y' is

   $y\; -\; z$

2. (ii) The sum of numbers x and y is (x + y). One-half of this sum is represented as

   $$\backslash frac\{1\}\{2\}(x\; +\; y)$$

3. (iii) The number z multiplied by itself means z × z, which is written as

   $z^2$

4. (iv) The product of numbers p and q is pq. One-fourth of this product is

   $$\backslash frac\{1\}\{4\}pq$$

5. (v) Squaring x gives x², and squaring y gives y². Adding them together results in

   $$x^2\; +\; y^2$$

6. (vi) The product of m and n is mn. Three times this product is 3mn. Adding 5 to this gives

   $3mn\; +\; 5$

7. (vii) The product of numbers y and z is yz. Subtracting this product from 10 gives

   $10\; -\; yz$

8. (viii) The sum of numbers a and b is (a + b). Their product is ab. Subtracting the sum from the product results in

   $$ab\; -\; (a\; +\; b)$$

We will identify the terms and their factors for each expression. Tree diagrams help visualize how terms are broken down into their factors.

(i) Tree Diagram Representation:

(a) Expression: $x\; -\; 3$

Terms: x, -3

Factors of x: x

Factors of -3: -1, 3

(b) Expression: $1\; +\; x\; +\; x^2$

Terms: 1, x, x²

Factors of 1: 1

Factors of x: x

Factors of x²: x, x

(c) Expression: $y\; -\; y^3$

Terms: y, -y³

Factors of y: y

Factors of -y³: -1, y, y, y

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

Terms: $5xy^2$, $7x^2y$

Factors of $5xy^2$: 5, x, y, y

Factors of $7x^2y$: 7, x, x, y

(e) Expression: $-ab\; +\; 2b^2\; -\; 3a^2$

Terms: $-ab$, $2b^2$, $-3a^2$

Factors of $-ab$: -1, a, b

Factors of $2b^2$: 2, b, b

Factors of $-3a^2$: -3, a, a

(ii) Identifying Terms and Factors:

(a) Expression: $-4x\; +\; 5$

Terms: $-4x$, 5

Factors of $-4x$: -4, x

Factors of 5: 5

(b) Expression: $-4x\; +\; 5y$

Terms: $-4x$, $5y$

Factors of $-4x$: -4, x

Factors of $5y$: 5, y

(c) Expression: $5y\; +\; 3y^2$

Terms: $5y$, $3y^2$

Factors of $5y$: 5, y

Factors of $3y^2$: 3, y, y

(d) Expression: $xy\; +\; 2x^2y^2$

Terms: $xy$, $2x^2y^2$

Factors of $xy$: x, y

Factors of $2x^2y^2$: 2, x, x, y, y

(e) Expression: $pq\; +\; q$

Terms: $pq$, q

Factors of $pq$: p, q

Factors of q: q

(f) Expression: $1.2ab\; -\; 2.4b\; +\; 3.6a$

Terms: $1.2ab$, $-2.4b$, $3.6a$

Factors of $1.2ab$: 1.2, a, b

Factors of $-2.4b$: -2.4, b

Factors of $3.6a$: 3.6, a

(g) Expression: $\backslash frac\{3\}\{4\}x\; +\; \backslash frac\{1\}\{4\}$

Terms: $\backslash frac\{3\}\{4\}x$, $\backslash frac\{1\}\{4\}$

Factors of $\backslash frac\{3\}\{4\}x$: $\backslash frac\{3\}\{4\}$, x

Factors of $\backslash frac\{1\}\{4\}$: $\backslash frac\{1\}\{4\}$

(h) Expression: $0.1p^2\; +\; 0.2q^2$

Terms: $0.1p^2$, $0.2q^2$

Factors of $0.1p^2$: 0.1, p, p

Factors of $0.2q^2$: 0.2, q, q