SOLUTION: Can you please help with the following problem, i am really struggling: Multiply and simplify: (2𝑥^2 + 3𝑥 + 6)(6𝑥^2 + 𝑥 − 6) Thanks

Algebra ->  Graphs -> SOLUTION: Can you please help with the following problem, i am really struggling: Multiply and simplify: (2𝑥^2 + 3𝑥 + 6)(6𝑥^2 + 𝑥 − 6) Thanks      Log On


   

Question 1093852: Can you please help with the following problem, i am really struggling:
Multiply and simplify: (2𝑥^2 + 3𝑥 + 6)(6𝑥^2 + 𝑥 − 6)
Thanks
Found 3 solutions by Alan3354, MathTherapy, Theo:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Multiply and simplify: (2𝑥^2 + 3𝑥 + 6)(6𝑥^2 + 𝑥 − 6)
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= 2x^2*(6𝑥^2 + 𝑥 − 6) + 3x*(6𝑥^2 + 𝑥 − 6) + 6*(6𝑥^2 + 𝑥 − 6)
= 12x^4 + 2x^3 - 12x^2 + 18x^3 + 3x^2 - 18x + 12x^2 + 6x - 36
= 12x^4 + 20x^3 + 3x^2 - 12x - 36
========================
2 different answers.
You figure out which is correct.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Can you please help with the following problem, i am really struggling:
Multiply and simplify: (2𝑥^2 + 3𝑥 + 6)(6𝑥^2 + 𝑥 − 6)
Thanks
highlight_green%2812x%5E4+%2B+20x%5E3+%2B+27x%5E2+-+12x+-+36%29

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
you use the distributive law of multiplication.

that law states:

a * (b + c) = a*b + a*c

(a + b) * (c + d) = a*c + a*d + b*c + b*d

here's my worksheet using this law on your problem.

$$$

$$$

this particular problem would generically be as follows: 



(a + b + c) * (d + e + f)


equals    a * (d + e + f) 
        + b * (d + e + f)
        + c * (d + e + f)


which equals     (a*d) + (a*e) + (a*f)
               + (b*d) + (b*e) + (b*f)
               + (c*d) + (c*e) + (c*f)


which equals     ad + ae + af
               + bd + be + bf
               + cd + ce + cf


the rest was just combining like terms.

to test if you did it correctly, then choose a random value for x and evaluate the original expression and the final expression.

if they both come up with the same answer, then you did good.

i used x = 25 and came up with 5016539 using both the original expression and the final expression, so i think i did good.