Question

1. simplify by using the distributive property and combining like terms

4(-5a² + 9b³) - 5b³ + 18a²

Explanation:

Step1: Distribute the division

First, we apply the distributive property of division over addition (or subtraction). The expression is \( 4(-5a^{2}+9b^{3})-5b^{3}+18a^{2} \)? Wait, no, looking at the image, maybe it's a typo, perhaps the original is \( 4(-5a^{2}+9b^{3})-5b^{3}+18a^{2} \). Let's correct the parsing. Let's assume the expression is \( 4(-5a^{2}+9b^{3})-5b^{3}+18a^{2} \).

First, distribute the 4:
\( 4\times(-5a^{2}) + 4\times(9b^{3}) - 5b^{3}+18a^{2} \)
\( = -20a^{2}+36b^{3}-5b^{3}+18a^{2} \)

Step2: Combine like terms for \(a^{2}\) terms

Combine the \(a^{2}\) terms: \( -20a^{2}+18a^{2} = (-20 + 18)a^{2} = -2a^{2} \)

Step3: Combine like terms for \(b^{3}\) terms

Combine the \(b^{3}\) terms: \( 36b^{3}-5b^{3} = (36 - 5)b^{3}=31b^{3} \)

Wait, maybe the original expression was misparsed. Let's re - examine the image. The user's image has "4(-5a² + 9b³) -5b³ +18a²". Let's redo:

Step1: Distribute 4

\( 4\times(-5a^{2})+4\times(9b^{3})-5b^{3}+18a^{2}=-20a^{2}+36b^{3}-5b^{3}+18a^{2} \)

Step2: Combine \(a^{2}\) terms

\( -20a^{2}+18a^{2}=(-20 + 18)a^{2}=-2a^{2} \)

Step3: Combine \(b^{3}\) terms

\( 36b^{3}-5b^{3}=(36 - 5)b^{3}=31b^{3} \)

So the simplified expression is \( -2a^{2}+31b^{3} \) or \( 31b^{3}-2a^{2} \)

Wait, maybe the original expression was different. If the expression was \( 4(-5a^{2}+9b^{3})-5b^{3}+18a^{2} \), the above steps are correct.

Answer:

\( 31b^{3}-2a^{2} \) (or \( -2a^{2}+31b^{3} \))