Question

Factors of x²/4-y^2/9 are​

Answer 1

Answer- The above question is from the chapter 'Algebra'.

Question: Factorise x²/4 - y²/9.

Solution: x²/4 - y²/9

We know that a² - b² = (a+b) (a-b) which is an algebraic identity.

Let a²= x²/4 and b²= y²/9

⇒ a= x/2 and b= y/3

Substituting the values,

x²/4 - y²/9

= (x/2 + y/3) (x/2 - y/3)

∴ Factors of x²/4 - y²/9 are:  (x/2 + y/3) (x/2 - y/3)

Answer 2

$\huge{\underline{\underline{\bf{Solution}}}}$

$\rule{200}{2}$

$\tt given\begin{cases} \sf{Polynomial : \frac{x^2}{4} - \frac{y^2}{9} } \end{cases}$

$\rule{200}{2}$

$\Large{\underline{\underline{\bf{To \: Find :}}}}$

We have to find the factors of the polynomial

$\rule{200}{2}$

$\Large{\underline{\underline{\bf{Explanation :}}}}$

$\sf{→\frac{x^2}{4} - \frac{y^2}{9}} \\ \\ \sf{→\frac{x^2}{(2)^2} - \frac{y^2}{(3)^2}} \\ \\ \sf{→\big(\frac{x}{2}\big)^2 - \big(\frac{y}{3} \big)^2}$

We know that,

$\Large{\implies{\boxed{\boxed{\sf{a^2 - b^2 = (a + b)(a - b)}}}}}$

$\sf{→\big(\frac{x}{2} + \frac{y}{3}\big)\big(\frac{x}{2} - \frac{y}{3}\big)}$