Algebraic Expressions in Maths Practice Question

An algebraic expression is a combination of numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division.

Example: 3x + 5 is an algebraic expression.

Solved Examples

Example 1: Find out the constant from the following algebraic expressions.

• x³ + 4x² - 6
• 9 + y⁵

Solution:

Constants are the terms that do not have any variable attached to them, therefore, in the first case, -6 is the constant, and in the second case, 9 is the constant.

Example 2: Find out the number of terms present in the following expressions.

• 4x² + 7x - 8
• 5y⁷ - 12

Solution:

Terms are separated by each other either by addition or subtraction sign. Therefore, in the first case, there are 3 terms and in the second case, there are 2 terms.

Example 3: Simplify the algebraic term, z⁵ + z³ - y⁶ + 7z⁵ - 8y + 34 + 10z³

Solution:

In the expression, there are terms with the same power and same variable that are repeated, first bring them together,

(z⁵ + 7z⁵) + (z³ + 10z³) - (y⁶ - 8y⁶) + 34.
= 8z⁵ + 11z³ - 9y⁶ + 34. (simplifying like terms)

Example 4: Add (13x² + 11), (-25x² + 26x + 42), and (-33x - 29).

Solution:

Let F = (13x² + 11) + ( – 25x² + 26x + 42) + (-33x – 29)
⇒ F = 13x² – 25x² + 26x – 33x + 11 + 42 – 29
⇒ F = -12x² – 7x + 24

Hence, (13x² + 11) + ( – 25x² + 26x + 42) + (-33x – 29) = -12x² – 7x + 24.

Example 5: Solve (5x + 4y + 6z)² + (3y – 7x)².

Solution:

Given, Let F = (5x + 4y + 6z)² + (3y – 7x)²

From algebraic formulae, we have

• (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca
• (a – b)² = a² – 2ab + b²

Thus, F = (5x)² + (4y)² + (6z)² + 2(5x)(4y) + 2(4y)(6z) + 2(6z)(5x) + [(3y)² – 2(3y)(7x) + (7x)²]
⇒ F= 25x² + 16y² + 36z² + 40xy + 48yz + 60zx +9y2 – 42xy + 49x²
⇒ F = 74x² + 25y² + 36z² – 2xy + 48yz + 60zx

Hence, (5x + 4y + 6z)² + (3y – 7x)² = 74x² + 25y² + 36z² – 2xy + 48yz + 60zx.

Unsolved Questions

Question 1: Find out the constant from the following algebraic expressions: 7x⁴−3x²+9

Question 2: Find the number of terms present in the following expressions. 6a²−5a+12

Question 3: Simplify: 4p + 7p − 6p + 5p − 9 + 12

Question 4: Solve (2x+y+3z)² + (x−5y)²