Question

pls answer question with photos​

Answer 1

$\bf{\large{\underline{\underline{Question:-}}}}$

Use suitable identities to find the following products

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

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

(iv) (y² + 3/2)(y² - 3/2)

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

$\bf{\large{\underline{\underline{Answer:-}}}}$

$\boxed{\sf{(i)\:(x + 4)(x + 10) = x^2 + 14x + 40}}$

$\boxed{\sf{(ii)\:(x + 8)(x - 10) = x^2 - 2x - 80}}$

$\boxed{\sf{(iv)\:(y^2 + \dfrac{3}{4} )(y^2 - \dfrac{3}{4} ) = y^4 - \dfrac{9}{4} }}$

$\boxed{\sf{(v)\:(3 - 2x)(3 + 2x) = 9 - 4x^2}}$

$\bf{\large{\underline{\underline{Explanation:-}}}}$

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

We know that (x + a)(x + b) = x² + (a + b)x + ab

Here x = x, a = 4, b = 10

By substituting the values in the identity we have,

= (x)² + (4 +10)x + 4(10)

= x² + 14x + 40

$\boxed{\bf{(i)\:(x + 4)(x + 10) = x^2 + 14x + 40}}$

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

It can be written as

= {x + 8}{x + (-10)}

We know that (x + a)(x + b) = x² + (a + b)x + ab

Here x = x, a = 8, b = - 10

By substituting the values in the identity we have,

= (x)² + {8 + (- 10)}x + 8(-10)

= x² + (8 - 10)x + (- 80)

= x² + (- 2)x - 80

= x² - 2x - 80

$\boxed{\bf{(ii)\:(x + 8)(x - 10) = x^2 - 2x - 80}}$

(iv) (y² + 3/2)(y² - 3/2)

We know that, (x + y)(x - y) = x² - y²

Here x = y², y = 3/2

By substituting the values in the identity we have,

= (y²)² - (3/2)²

$= y^{2*2} - \dfrac{3^2}{2^2}$

$= y^{4} - \dfrac{9}{4}$

$\boxed{\bf{(iv)\:(y^2 + \dfrac{3}{4} )(y^2 - \dfrac{3}{4} ) = y^4 - \dfrac{9}{4} }}$

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

We know that, (x - y)(x + y) = x² - y²

By substituting the values in the identity we have,

Here x = 3, y = 2x

= (3)² - (2x)²

= 9 - 2²(x²)

= 9 - 4(x²)

= 9 - 4x²

$\boxed{\bf{(v)\:(3 - 2x)(3 + 2x) = 9 - 4x^2}}$

$\bf{\large{\underline{\underline{Identities\:Used:-}}}}$

[1] (x + y)(x - y) = x² - y²

[2] (x + a)(x + b) = x² + (a + b)x + ab

$\bf{\underline{\underline{Note:-}}}$

(x + y)(x - y) = x² - y² or (x - y)(x + y) = x² - y² are same.