Question

Is (a-3)(2a^2 + 3a + 3) equivalent to 2(a^3 - 1.5a^2 - 3a - 4.5)

Answer 1

Answer: Yes they are equivalent

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Work Shown:

Expand out the first expression to get

(a-3)(2a^2 + 3a + 3)

a(2a^2 + 3a + 3) - 3(2a^2 + 3a + 3)

2a^3 + 3a^2 + 3a - 6a^2 - 9a - 9

2a^3 + (3a^2-6a^2) + (3a-9a) - 9

2a^3 - 3a^2 - 6a - 9

Divide every term by 2 so we can pull out a 2 through the distributive property

2a^3 - 3a^2 - 6a - 9 = 2(a^3 - 1.5a^2 - 3a - 4.5)

This shows that (a-3)(2a^2 + 3a + 3) is equivalent to 2(a^3 - 1.5a^2 - 3a - 4.5)

Answer 2

yes

Explanation:

(a-3)(2a^2 + 3a + 3) = a(2a^2 + 3a + 3) -3(2a^2 + 3a + 3)

= 2a^3 +3a^2 +3a -6a^2 -9a -9

= 2a^3 +a^2(3 -6) +a(3 -9) -9

= 2a^3 -3a^2 -6a -9

= 2(a^3 -1.5a^2 -3a -4.5) . . . . the form you're asking about