Question

(h + 9)(5h - 4h² - 10)

Explanation:

Step1: Distribute \( h \)

Multiply \( h \) with each term in \( 5h - 4h^2 - 10 \):
\( h \times 5h = 5h^2 \), \( h \times (-4h^2) = -4h^3 \), \( h \times (-10) = -10h \)
So we get \( 5h^2 - 4h^3 - 10h \)

Step2: Distribute \( 9 \)

Multiply \( 9 \) with each term in \( 5h - 4h^2 - 10 \):
\( 9 \times 5h = 45h \), \( 9 \times (-4h^2) = -36h^2 \), \( 9 \times (-10) = -90 \)
So we get \( 45h - 36h^2 - 90 \)

Step3: Combine like terms

Add the results from Step1 and Step2:
\( (5h^2 - 4h^3 - 10h) + (45h - 36h^2 - 90) \)
Combine \( h^3 \) terms: \( -4h^3 \)
Combine \( h^2 \) terms: \( 5h^2 - 36h^2 = -31h^2 \)
Combine \( h \) terms: \( -10h + 45h = 35h \)
Constant term: \( -90 \)

Answer:

\( -4h^3 - 31h^2 + 35h - 90 \)