Question

Simplify using the horizontal method (2n^2+5n+5)(2n-4)

Answer 1

(2n - 4)(2n^2 + 5n + 5) =
2n(2n^2 + 5n + 5) - 4(2n^2 + 5n + 5) =
4n^3 + 10n^2 + 10n - 8n^2 - 20n - 20 =
4n^3 + 2n^2 - 10n - 20 <===

Answer 2

( 2n² + 5n + 5 ) ( 2n - 4 ) = 4n³ + 2n² -10n -20

Explanation:

Given Expressions for Product: ( 2n² + 5n + 5 ) ( 2n - 4 )

To find: Product of the expression.

Consider,

( 2n² + 5n + 5 ) ( 2n - 4 )

⇒ 2n² ( 2n - 4 ) + 5n ( 2n - 4 ) + 5 ( 2n - 4 )

⇒ 2n² × 2n + 2n² × (-4) + 5n × 2n + 5n × (-4) + 5 × 2n + 5 × (-4)

⇒ 2 × 2 × n² × n + 2 × (-4) n² + 5 × 2 × n × n + 5 × (-4) n + 10n + (-20)

⇒ 4n³ + (-8)n² + 10n² + (-20)n + 10n -20

⇒ 4n³ - 8n² + 10n² - 20n + 10n -20

⇒ 4n³ +( -8 + 10 ) n² + ( -20 + 10 ) n -20

⇒ 4n³ + 2n² -10n -20

Therefore, ( 2n² + 5n + 5 ) ( 2n - 4 ) = 4n³ + 2n² -10n -20