Question

find the product of the question.​

Answer 1

GIVEN :-

• (x/2 - 3y) (3y + x/2) (x²/4 + 9y²)

TO FIND :-

• The product

SOLUTION :-

⇒ [(x/2 - 3y) (3y + x/2)] (x²/4 + 9y²)

⇒ [x/2(3y + x/2) - 3y(3y + x/2)] (x²/4 + 9y²)

⇒ [(3xy)/2 + x²/4 - 9y² - (3xy)/2] (x²/4 + 9y²)

⇒ [(3xy)/2 + x²/4 - 9y² - (3xy)/2] (x²/4 + 9y²)

⇒ (x²/4 - 9y²) (x²/4 + 9y²)

⇒ [x²/4(x²/4 + 9y²) - 9y²(x²/4 + 9y²]

⇒ [x⁴/16 + (9x²y²)/4 - (9x²y²)/4 - 81y⁴]

⇒ x⁴/16 - 81y⁴

ADDITIONAL INFORMATION :-

⇒ ( x + y )² = x² + 2xy + y²

⇒ ( x - y )² = x² - 2xy + y²

⇒ ( x + a ) ( x + b ) = x² + x ( a + b ) + ab

⇒ ( a + b ) ( a - b ) = a² - b²

⇒ ( a + b ) ( a + b ) = ( a + b )²

Answer 2

Question:

Find the product of

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

To find:

★ To find the product of the given expression.

Answer:

$The \: value \: is \: \underline{ \: \sf \pink { {x}^{4} - 36 {y}^{4} } \: }$

Given:

★ An expression is given,

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

Step-by-step explanation:

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

$=\big(\frac{x - 6y}{2} \big)\big( \frac{6y + x}{2} \big)\big( \frac{ {x}^{2} + 36 {y}^{2} }{4} )$

L.C.M. is 4

$= \frac{[2(x - 6y) \times 2(6y + x)] \times ( {x}^{2} + 36 {y}^{2}) }{4}$

Now simplifying,

$\bigstar (x - 6y)(6y + x)$

It also can be written as,

$\implies (x - 6y)(x + 6y)$

$It's \: of \: the \: form \:\\ \boxed{ ( {a}^{2} - {b}^{2} ) = (a - b)(a + b)}$

$\implies \underline{ ( {x}^{2} - {6y}^{2} )}$

$\bigstar( {x}^{2} + 36 {y}^{2} )$

It also can be written as,

$\implies {(x)}^{2} + {(6y)}^{2}$

$It's \: of \: the \: form \: \\\boxed{ ( {a}^{2} + {b}^{2} ) = {(a + b)}^{2} - 2ab }$

$= \frac{ \not{4}[( {x}^{2} - {(6y)}^{2}( {x}^{2} + {(6y)}^{2} }{ \not{4}}$

$= ( {x}^{2} - 6 {y}^{2} )( {x}^{2} + 6 {y}^{2} )$

$It's \: of \: the \: form \: \underline{ ( {a}^{2} - {b}^{2} )}$

$= \boxed{ {x}^{4} - 36 {y}^{4} }$

$\therefore The \: value \: is \: \underline{ \: \sf \pink{ \bold{{x}^{4} - 36 {y}^{4}} } \: }$

Formulae used:

$\bigstar ( {a}^{2} - {b}^{2} ) = (a - b)(a + b)$

$\bigstar {(a + b)}^{2} = {a}^{2} + 2ab + {b}^{2}$

Formulae to know:

$\bigstar {(a - b)}^{2} = {a}^{2} - 2ab + {b}^{2}$

$\bigstar {a}^{3} + {b}^{3} = (a + b)( {a}^{2} - ab + {b}^{2} )$

$\bigstar {a}^{3} - {b}^{3} = (a - b)( {a}^{2} + ab + {b}^{2} )$

$\bigstar (x + a)(x + b) = {x}^{2} + (a + b)x + ab$