Question

use identity ( x + a ) ( x + b) = x² + ( a + b) x + ab to find the product of the following . (1) ( x + 3 ) ( x + 7 ) . (2) ( 2a² + a) ( 2a² + 5 ) ​

Answer 1

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

We have to find the product

1) ( x + 3 ) ( x + 7 )

$\boxed{\bf{[ (x+a) (x+b)=x² + ( a + b) x + ab ]}}$

$\sf\implies\:{(x+3)(x+7)}$

$\sf{➝\;x²+(7+3)x+7\times3}$

$\sf{➝\;x^2+10x+21}$

Thus ,

( x + 3 ) ( x + 7 ) = x ²+ 10 x +21

2) ( 2a² + a) ( 2a² + 5 )

Now , use identity [ (x+a) (x+b)=x² + ( a + b) x + ab ]

Then ,

$\sf\implies{(2a^2+a)(2a^2+5)}$

$\sf{➝\;(2a^2)^2+(a+5)(2a^2)+5\times\:a}$

$\red{\sf{☞\;4a^4+2a^3+10a^2+5a=4a}}$

Hope It Helps You ✌️

Answer 2

Answer:

$We have to find the product</p><p>1) ( x + 3 ) ( x + 7 )</p><p>\boxed{\bf{[ (x+a) (x+b)=x² + ( a + b) x + ab ]}}[(x+a)(x+b)=x²+(a+b)x+ab]</p><p>\sf\implies\:{(x+3)(x+7)}⟹(x+3)(x+7)</p><p>\sf{➝\;x²+(7+3)x+7\times3}➝x²+(7+3)x+7×3</p><p>\sf{➝\;x^2+10x+21}➝x2+10x+21</p><p>Thus ,</p><p>( x + 3 ) ( x + 7 ) = x ²+ 10 x +21</p><p>2) ( 2a² + a) ( 2a² + 5 )</p><p>Now , use identity [ (x+a) (x+b)=x² + ( a + b) x + ab ]</p><p>Then ,</p><p>\sf\implies{(2a^2+a)(2a^2+5)}⟹(2a2+a)(2a2+5)</p><p>\sf{➝\;(2a^2)^2+(a+5)(2a^2)+5\times\:a}➝(2a2)2+(a+5)(2a2)+5×a</p><p>\red{\sf{☞\;4a^4+2a^3+10a^2+5a=4a}}☞4a4+2a3+10a2+5a=4a</p><p>Hope It Helps You ✌️</p><p>$