Question

PLS HELP ME!!
I really need the answers to these last few questions to a practice sheet I need to turn them in ASAP. I just cannot seem to understand these last ones!

Simplify each polynomial. Write each in standard form.
HINT: Watch for the operation! Add? Subtract? Or Multiply?
8. 4m(2m+9m^2-6)

9. q(11+8q-2q^2 )

12. (x-1)^2

13. (4y+2)^2

Answer 1

8. 4m(2m+9m^2-6)
Distribute Parenthesis -> 4m · 2m + 4m · 9m^2 + 4m(-6)
Multiply -> 4 · 2mm + 4 · 9m^2m - 4 · 6m
Simplify -> 36m^3 + 8m^2 - 24m

9. q(11+8q-2q^2 )
Distribute Parenthesis -> q · 11 + q · 8 + q(-2q^2)
Multiply -> 11q · + 8qq - 2q^2q
Simplify -> -2q^3 +8q^2 + 11q

12. (x-1)^2
This is a perfect square so you can just use the formula:
(a-b)^2 = a^2 -2ab + b^2 (a = x and b = 1)
(x-1)^2 = x^2 - 2(x)(1) + 1^2
Simplify: x^2 - 2x + 1

13. (4y+2)^2
This is also a perfect square formula!
See if you can solve this one using the formula I gave you.

Hope this helps!

Answer 2

8.

4 m ( 2 m + 9 m² - 6 ) =

4 m ∙ 2 m + 4 m ∙ 9 m² - 4 m ∙ 6 =

8 m² + 36 m³ - 24 m =

36 m³ + 8 m² - 24 m


9.

q ( 11 + 8 q - 2 q² ) =

q ∙ 11 + q ∙ 8 q - q ∙ 2 q² =

11 q + 8 q² - 2 q³ =

- 2 q³ + 8 q² + 11 q

___________________________

Remark for queastions 12 and 13:

( a ± b )² = a² ± 2 ∙ a ∙ b + b²
___________________________

12.

( x - 1 )² = x² - 2 ∙ x ∙ 1 + 1² = x² - 2 x + 1

13.

( 4 y + 2 )² = ( 4 y )² + 2 ∙ 4 y ∙ 2 + 2² = 16 y² + 16 y + 4