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
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!
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
I'd be happy to help you with these polynomial simplification questions! Understanding how to simplify polynomials will be useful to you, so let's go through them step by step.
First, let's start with question 8:
8. 4m(2m+9m^2-6)
To simplify this expression, we need to perform the multiplication and distribute the 4m to every term inside the parentheses. Remember, when you multiply a number or a variable with a term in parentheses, you multiply the number or variable by each term inside the parentheses.
So let's simplify this expression:
4m(2m+9m^2-6)
= 4m * 2m + 4m * 9m^2 - 4m * 6
= 8m^2 + 36m^3 - 24m
Therefore, the simplified form of 4m(2m+9m^2-6) is 8m^2 + 36m^3 - 24m.
Moving on to question 9:
9. q(11+8q-2q^2)
Similar to the previous question, we need to distribute the q to every term inside the parentheses. Let's simplify it:
q(11+8q-2q^2)
= q * 11 + q * 8q - q * 2q^2
= 11q + 8q^2 - 2q^3
The simplified form of q(11+8q-2q^2) is 11q + 8q^2 - 2q^3.
Now, let's move on to question 12:
12. (x-1)^2
To simplify this expression, we need to square the entire expression inside the parentheses. This can be done by multiplying the expression by itself:
(x-1)^2 = (x-1)(x-1)
To simplify, we can use the FOIL method or the distributive property. Let's use the distributive property:
(x-1)(x-1) = x(x-1) - 1(x-1)
= x^2 - x - x + 1
= x^2 - 2x + 1
Therefore, the simplified form of (x-1)^2 is x^2 - 2x + 1.
Finally, question 13:
13. (4y+2)^2
Similarly to the previous question, we need to square the entire expression inside the parentheses:
(4y+2)^2 = (4y+2)(4y+2)
Using the distributive property, let's simplify it:
(4y+2)(4y+2) = 4y(4y+2) + 2(4y+2)
= 16y^2 + 8y + 8y + 4
= 16y^2 + 16y + 4
So, the simplified form of (4y+2)^2 is 16y^2 + 16y + 4.
I hope that helps! Remember, understanding how to simplify polynomials can be beneficial, so it's worth spending some time practicing these types of problems to improve your skills.