Algebraic Expressions Class 7 Worksheet Maths Chapter 10

Ans: 
(a) Step 1: Simplify inside the innermost parentheses:
(x−2y) = x − 2y
Now substitute this into the expression:
2x − {5y − (x − 2y)} = 2x − {5y − x + 2y}
Step 2: Simplify inside the curly braces by combining like terms:
5y−x + 2y = 7y − x
Now substitute this back:
2x − (7y − x)
Step 3: Distribute the negative sign:
2x − 7y + x
Step 4: Combine like terms:
(2x + x) − 7y = 3x − 7y
Final answer:
3x − 7y

(b) 5a−{3a−(2−a)+4}
Step 1: Start by simplifying the inner parentheses.
(2 − a)
There's nothing to simplify, so it remains as $2\; -\; a$2 − a.
Step 2: Substitute $2\; -\; a$2 − a back into the expression.

5a − {3a − (2 − a) + 4}=5a−{3a − 2 + a + 4}

We distributed the negative sign over $2\; -\; a$2 − a.

Step 3: Simplify the expression inside the curly brackets.

3a − 2 + a + 4 = 4a + 2
Step 4: Now subtract $4a+24a\; +\; 2$4a+2 from $5a5a$5a.
$5a\; -\; (4a\; +\; 2)\; =\; 5a\; -\; 4a\; -\; 2$5a − (4a + 2) = 5a − 4a − 2
Step 5: Combine like terms.
a − 2
Thus, the simplified expression is:
a − 2

Ans. Given:

• Daily spending = ₹x
• Daily savings = ₹y
• Duration = 3 weeks = 21 days (since 1 week = 7 days)

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.
Step-by-step solution:

Substitute 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. 3

Ans. 

Step 1: Write the expression for the sum.
We are asked to find the sum of:
(3x − y + 11) and (−y − 11)
Adding the two expressions:
(3x − y + 11) + (−y − 11)
Simplifying:
3x − y + 11 −y − 11
Combine like terms:
3x − 2y

Step 2: Subtract the expression $3x\; -\; y\; -\; 11$3x − y − 11 from the sum.
We now subtract (3x − y − 11) from the result $3x\; -\; 2y$3x − 2y.
(3x − 2y) − (3x − y − 11)
Simplifying:
3x − 2y − 3x + y + 11
Combine like terms:
−y + 11
Final Answer:
The result is:
$\backslash boxed\{-y\; +\; 11\}$−y + 11

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 $aa$a, $bb$b, and $cc$c.
So, the numerical coefficient is $\backslash boxed\{-5\}$−5.

Ans. 2a² + ab + 3, 38

Ans. 10x²y

Ans. 

R.H.S. =

  = L.H.S. = R.H.S

Ans. 2ab – b²

Ans. Length = 54 m, Breadth = 20 m

Ans. 8 m² – 11 m + 10

Ans. a³ – 5a² + 7a – 7

Ans. Each of base angle = 45° Vertex angle = 90° 45°, 45° & 90°

Ans. 50 Paise coins = 20

25 Paise coins = 80