Science & Math Question World : Class 7 CBSE Worksheet: Algebraic Expressions

Fill in the blanks:
a) In the expression $5 x + 7$ , the coefficient of $x$ is ______.
b) A term that does not contain a variable is called a ______.
Identify the terms, coefficients, and constants in the following expressions:
a) $2 x + 5$
b) $7$
Write an algebraic expression for the following statements:
a) The sum of a number $x$ and 9.
b) 5 times a number $y$ subtracted from 20.
c) The product of a number $p$ and 7 increased by 15.

Simplify:
a) $3 x + 5 x$
b) $7 a - 4 + 2 a + 8$
c) $4 p^{2} + 3 p - 2 p$
Add the following:
a) $3 x + 4$ , $5 x - 7$ , $2 x + 6$
b) $2 a^{2} + 3 a - 5$ and $4 a^{2} - 2 a + 6$
Subtract:
a) $(6 x + 8) - (3 x - 5)$
b) $(5 a^{2} - 3 a + 4) - (2 a^{2} + a - 6)$

Write the expression for the following situations:
a) Rohan’s age is 5 years more than twice his brother’s age. If his brother’s age is $x$ , what is Rohan’s age?
b) The cost of a pen is $x$ rupees, and the cost of a notebook is $3 x + 5$ rupees. Write an expression for the total cost of 3 pens and 2 notebooks.
The perimeter of a rectangle is given by $2 (l + b)$ . If the length is $3 x$ and the breadth is $x + 2$ , find the expression for its perimeter.

Factorize the following expressions:
a) $4 x + 8$
b) $6 a^{2} b + 9 a b^{2}$
Group the terms and factorize:
a) $3 x + 6 + 2 x y + 4 y$
b) $5 a^{2} - 10 a b + 15 b^{2}$

Simplify and evaluate when $x$
a) $3x^2 + 5x - 7$
b) $2(x + 3)^2 - 4(x - 2)$
The sum of two numbers is $5 x + 3$ , and one of the numbers is $2 x + 1$ . Find the other number.

Instructions:

Match the following:
a) $7x^2$ → (i) Constant term
b) $3a + 5b$ → (ii) Monomial
c) $5$ → (iii) Polynomial
d) $x^2 + 2x + 3$ → (iv) Binomial
Write the terms and their coefficients in the following expressions:
a) $4x - 7$
b) $2a^2 + 3ab - 8b^2$
Write the expression for:
a) A number $x$ divided by 5 and then added to 7.
b) Twice the sum of a number $y$ and 3.

Simplify:
a) $5x + 3 - 7x + 8$
b) $4 a^{2} + 6 a - 3 a^{2}$
c) $2x(x + 3) - 3(x^2 - x)$
Subtract the second expression from the first:
a) $8x + 5$ and $3x - 7$
b) $4a^2 - 2ab + b^2$ and $3a^2 + ab - 2b^2$
Add:
a) $7x + 3$ , $2x - 5$ , and $-x + 7$
b) $2p^2 + 3pq - 5q^2$ and $4p^2 - 2pq + q^2$

Form expressions for the following:
a) Priya’s current age is $x$ years. Write an expression for her age 5 years ago and 3 years later.
b) The length of a rectangle is $4x + 2$ and its breadth is $2x - 1$ . Write an expression for its area.
The total cost of $x$ pens and $y$ notebooks is given by $10x + 15y$ . Write expressions for:
a) The cost of 3 pens and 4 notebooks.
b) The cost of 5 pens and 2 notebooks.

Simplify and evaluate when $x = 3$
a) $2x^2 + 5x - 4$
b) $3(x - 2)^2 - 4(x + 1)$
Ramesh bought $x$ notebooks and $y$ pens for a total cost of $5x + 2y$ . He later bought 2 more notebooks and 3 more pens. Write an expression for the total cost of his purchase.
The perimeter of a triangle is given as $3x + 2y$ . If two sides of the triangle are $x + y$ and $2x - y$ , find the expression for the third side.

Science & Math Question World