Question

Using suitable identity, find the products of the following
(i) (x+4)(x+10)
(ii) (x+8)(x-10)
(iii) (3x+4)(3x-5)
(iv) (y^2 + 3/2)(y^2 - 3/2)
(v) (3-2x) (3+2x)

Answer 1

see ur answer in pic ..

Hope it's helps you..✌✔

Answer 2

$\mathbb{ANSWER}$:

(i) (x + 4) (x + 10)

$\bf{Usinga\: identity}$ : (x + a) (x + b) = x² + (a+b)x + ab
Here,
x = x , a = 4 , b = 10

=> (x)² + (4 + 10)x + 4*10
=> x² + 14x + 40

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(ii) (x + 8) (x - 10)

$\bf{Using\: identity}$ : (x + a) (x + b) = x² + (a+b)x + ab
Here,
x = x , a = 8 , b = (-10)

=> (x)² + { 8 + (-10) }x + 8*(-10)
=> x² + (8 - 10)x - 80
=> x² - 2x - 80

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(iii) (3x + 4) (3x - 5)

$\bf{Using\: identity}$ : (x + a) (x + b) = x² + (a+b)x + ab
Here,
x = 3x , a = 4 , b = (-5)

=> (3x)² + { 4 + (-5) }*3x + 4*(-5)
=> 9x² + (4 - 5)*3x - 20
=> 9x² + (-1)*3x - 20
=> 9x² - 3x - 20

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(iv) (y² + $\frac{3}{2}$) (y² - $\frac{3}{2}$)

$\bf{Using\: identity}$ : (x + a) (x + b) = x² + (a+b)x + ab
Here,
x = y² , a = $\frac{3}{2}$ , b = (-$\frac{3}{2}$)

=> (y²)² + { $\frac{3}{2}$ + (- $\frac{3}{2}$ }*y² + $\frac{3}{2}$*(- $\frac{3}{2}$)

=> $\ {y}^{4}$ + ($\frac{3}{2}$ - $\frac{3}{2}$ )*y² + (- $\frac{9}{4}$)

=> $\ {y}^{4}$ + 0*y² - $\frac{9}{4}$

=> $\ {y}^{4}$ - $\frac{9}{4}$

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(v) (3 - 2x) (3 + 2x)

$\bf{Using \:identity}$ : (x + a) (x + b) = x² + (a+b)x + ab
Here,
x = 3 , a = (-2x) , b = 2x

=> (3)² + { (-2x) + 2x }*3 + (-2x)*2x
=> 9 + 0*3 + (-4x²)
=> 9 - 4x²
=> - 4x² + 9