Worksheet Question & Answers : Algebraic Expressions

Ans: Algebraic expressions in the following: 

1. Twice the difference of numbers $a$a and $b$b:
   Expression: $2(a\; -\; b)$2(a-b)

2. Three-fourths of the sum of numbers $p$p and q:
   Expression: $\frac{3}{4}(p+q)\backslash frac\{3\}\{4\}(p\; +\; q)$

3. The square of the product of $x$x and y:
   Expression: $(xy)^2$(xy)²

Ans.Given:

Total income per day:
Pallavi's total daily income is the sum of her daily spending and savings:
Daily income = Daily spending + Daily savings = ₹x + ₹y
Total income after 3 weeks (21 days):
To find her income after 3 weeks, multiply her daily income by the number of days (21):
Total income = (₹x + ₹y) × 21
Thus, Pallavi's income after 3 weeks is:
21(x + y)

Ans.We are given P = -10, and we need to find the value of the expression P² - 2P - 100.

Substituting P = -10 into the expression:

$^2\; -\; 2P\; -\; 100\; =\; (-10)^2\; -\; 2(-10)\; -\; 100$P² - 2P - 100 = (-10)² - 2(-10) -100

Simplify each term:

-2(-10) = 20
Sothe expression becomes:
$100\; +\; 20\; -\; 100$100 + 20 - 100

Simplify the result:

100 + 20 - 100 = 20

Thus, the value of $P^2\; -\; 2P\; -\; 100$P² - 2P - 100 is 20

Ans.

1. 6x²y → Monomials
2. $3a\mathrm{<sup\; style="word-break:break-word;line-height:1.8;font-family:lato,sans-serif;font-size:13px\; !important;letter-spacing:inherit">2</sup>}+7\mathrm{ba\; +\; 7b\; \to \; Trinomial}$
3. $\mathrm{p\; -\; q\; +\; r\; \to \; Trinomial }$
4. 8mn-4p → Binomial 
5. 4a²b → Monomials

Ans.

(i)Given -3x²

The coefficient of x² is -3.

(ii)Given 5x²yz

The coefficient of x² is 5yz.

(iii)Given 5/7x²z

The coefficient of x² is 5/7z.

(iv)Given (-3/2) ax² + yx

The coefficient of x² is - (3/2) a.

Ans.

(i) xy

There is no visible number, but it is understood to be $1$1.
So, the numerical coefficient is $oxed\{1\}$1.

(ii) -3xy

The numerical coefficient is the number $3$-3 multiplying the variables.
So, the numerical coefficient is -3.

(iii) 2p³

The numerical coefficient is the number $2$2 multiplying the variable p³.
So, the numerical coefficient is $\backslash boxed\{2\}$2.

(iv) -5abc

The numerical coefficient is -5, which multiplies the variables a, b, and $c$c.
So, the numerical coefficient is $\backslash boxed\{-5\}$-5.

Ans. Given: 2(a + ab) + 3 - ab 
Expand the terms:
= 2a + 2ab + 3 - ab
Combine like terms:
= 2a + ab + 3
Substitute:
a = 5, b = -3
= 2(5) + (5)(-3) + 3

Simplify:
= 10 - 15 + 3

= -2

Ans.Since all the terms have the same variables (x²y), we can add them all directly:

4x²y + 8x²y +(-2x²y)

=10x²y
Substituting values x = 1 and y = -2.
= 10(1)²(-2)
=-20

Ans.

(i) Given x = -2, y = -1, z = 3

Consider (x/y) + (y/z) + (z/x)

On substituting the given values we get,

= (-2/-1) + (-1/3) + (3/-2)

The LCM of 3 and 2 is 6

= (12 - 2 - 9)/6

= (1/6)

(ii) Given x = -2, y = -1, z = 3

Consider x² + y² + z² - xy - yz - zx

On substituting the given values we get,

= (-2)² + (-1)² + 3² - (-2) (-1) - (-1) (3) - (3) (-2)

= 4 + 1 + 9 - 2 + 3 + 6

= 23 - 2

= 21

Ans.

(i) Given x = 1, y = -1, z = 2, a = -2, b = 1, c = -2

Consider ax + by + cz

On substituting the given values

= (-2) (1) + (1) (-1) + (-2) (2)

= -2 - 1 - 4

= -7

(ii) Given x = 1, y = -1, z = 2, a = -2, b = 1, c = -2

Consider ax² + by² - cz

On substituting the given values

= (-2) × 1² + 1 × (-1)² - (-2) × 2

= -2 + 1 - (-4)

= -1 + 4

= 3