# Prove that the factor of ${(2n + 3)^2} - {(2n - 3)^2}$ is 8, where n is a natural number.

Answer

Verified

381.3k+ views

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.

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.

Recently Updated Pages

Define absolute refractive index of a medium

Find out what do the algal bloom and redtides sign class 10 biology CBSE

Prove that the function fleft x right xn is continuous class 12 maths CBSE

Find the values of other five trigonometric functions class 10 maths CBSE

Find the values of other five trigonometric ratios class 10 maths CBSE

Find the values of other five trigonometric functions class 10 maths CBSE

Trending doubts

State Gay Lusaaccs law of gaseous volume class 11 chemistry CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

What is BLO What is the full form of BLO class 8 social science CBSE

What is pollution? How many types of pollution? Define it

Change the following sentences into negative and interrogative class 10 english CBSE

Which is the tallest animal on the earth A Giraffes class 9 social science CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

How fast is 60 miles per hour in kilometres per ho class 10 maths CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE