CBSE Class 7 Mathematics Chapter 12: Algebraic Expressions NCERT Solutions

1. Subtraction of z from y: When we subtract z from y, the expression is written as $y\; -\; z$.
2. One-half of the sum of numbers x and y: The sum of x and y is $x\; +\; y$. One-half of this sum is $\backslash frac\{1\}\{2\}(x\; +\; y)$.
3. The number z multiplied by itself: When a number is multiplied by itself, it is squared. So, z multiplied by itself is $z\; \backslash times\; z\; =\; z^2$.
4. One-fourth of the product of numbers p and q: The product of p and q is $pq$. One-fourth of this product is $\backslash frac\{1\}\{4\}pq$.
5. Numbers x and y both squared and added: Squaring x gives $x^2$ and squaring y gives $y^2$. Adding them together results in the expression $x^2\; +\; y^2$.
6. Number 5 added to three times the product of m and n: The product of m and n is $mn$. Three times this product is $3mn$. Adding 5 to this gives $3mn\; +\; 5$.
7. Product of numbers y and z subtracted from 10: The product of y and z is $yz$. Subtracting this product from 10 is written as $10\; -\; yz$.
8. Sum of numbers a and b subtracted from their product: The product of a and b is $ab$. The sum of a and b is $a\; +\; b$. Subtracting the sum from the product gives $ab\; -\; (a\; +\; b)$.

(i) Identifying terms and factors using tree diagrams:

1. Expression: $x-3$

   Terms: $x$, $-3$

   Factors of $x$: $x$

   Factors of $-3$: $-1,\; 3$

2. Expression: $1\; +\; x\; +\; x^2$

   Terms: $1$, $x$, $x^2$

   Factors of $1$: $1$

   Factors of $x$: $x$

   Factors of $x^2$: $x,\; x$

3. Expression: $y\; -\; y^3$

   Terms: $y$, $-y^3$

   Factors of $y$: $y$

   Factors of $-y^3$: $-1,\; y,\; y,\; y$

4. Expression: $5xy^2\; +\; 7x^2y$

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

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

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

5. 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:

1. Expression: $-4x+5$

   Terms: $-4x$, $5$

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

   Factors of $5$: $5$

2. Expression: $-4x\; +\; 5y$

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

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

   Factors of $5y$: $5,\; y$

3. Expression: $5y\; +\; 3y^2$

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

   Factors of $5y$: $5,\; y$

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

4. Expression: $xy\; +\; 2x^2y^2$

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

   Factors of $xy$: $x,\; y$

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

5. Expression: $pq+q$

   Terms: $pq$, $q$

   Factors of $pq$: $p,\; q$

   Factors of $q$: $q$

6. 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 $3.6a$: $3.6,\; a$

7. 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 $\backslash frac\{1\}\{4\}$: $\backslash frac\{1\}\{4\}$

8. 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 $0.2q^2$: $0.2,\; q,\; q$