 Questions & Answers    Question Answers

# Prove that the factor of ${(2n + 3)^2} - {(2n - 3)^2}$ is 8, where n is a natural number.  Answer Verified
Hint: Use algebra to solve the expression by applying the general formula of $a^2 - b^2$.
We have given the expression ${(2n + 3)^2} - {(2n - 3)^2}$ . Observe its in the form of ${a^2} - {b^2}$ where, $a = {(2n + 3)^2},b = {(2n - 3)^2}$ and we can use the formula ${a^2} - {b^2} = (a + b)(a - b)$ . Using the formula, we’ll get
$\ {(2n + 3)^2} - {(2n - 3)^2} \\ = (2n + 3 + 2n - 3)(2n + 3 - 2n + 3){\text{ [}}{a^2} - {b^2} = (a + b)(a - b){\text{]}} \\ {\text{ = (4n)(6)}} \\ {\text{ = 24n}} \\ \$
Since, it’s nothing but 24n so we can easily write it in terms of 8 as $24n = 8(3n)$ and hence we can conclude that 8 is the factor of given expression.

Note: In this question, just follow it and using the fundamentals of algebra, we can solve it but we need to be careful with the calculation part.
Bookmark added to your notes.
View Notes
Table of 32 - Multiplication Table of 32  Factors of 32  The Difference Between an Animal that is A Regulator and One that is A Conformer  Factor of 415  All that Glitters is not Gold Essay  Algebra Formula for Class 10  Factor Theorem  Scale Factor  Integrating Factor  Algebraic Formulas for Class 8  