## calculusxy one year ago factoring quadratic expression...

1. calculusxy

$\huge 294a^2 - 54$

2. calculusxy

@Nnesha

3. calculusxy

@jim_thompson5910 @hartnn @Jhannybean

4. calculusxy

$\large 294a^2 - 0a - 54$

5. anonymous

larget common factor of $$294$$ and $$24$$ is?

6. anonymous

get rid of that stupid zero

7. calculusxy

okay sorry

8. calculusxy

don't you mean the gcf of 294 and 54 ?

9. anonymous

yes i get 6

10. Jhannybean

Hahahaha

11. anonymous

so start with $6(49a^2-9)$ then factor $49a^2-9$ as the difference of two squares

12. Jhannybean

$a^2-b^2 = (a-b)(a+b)$

13. calculusxy

(7a + 3)(7a - 3)

14. Jhannybean

or rather,.... $$ca^2-b^2 = (ca-b)(ca+b)$$ :') $$c$$ is the coefficient of one of the terms lol

15. anonymous

$\heartsuit^2-\spadesuit^2=(\heartsuit+\spadesuit)(\heartsuit -\spadesuit)$[

16. Jhannybean

Oh you think you're fancy huh

17. anonymous

just showing off

18. Jhannybean

lol

19. anonymous

$\xi^2 -\omega^2=(\xi+\omega)(\xi-\omega)$

20. Jhannybean

You are correct @calculusxy , just don't forget to multiply by the 6

21. calculusxy

can i make sure the answer to another question?

22. calculusxy

$\large 12x^2 + 12x + 3$ $\huge Answer$ $\large 3(2x+1)(2x+1)$

23. anonymous

looks good to me you @Jhannybean ?

24. calculusxy

well i did the same question, but in a different way and got a different answer ( can u catch my mistake) 12x^2 + 12x + 3 12x^2 + 6x + 6x + 3 2x(2x+3) 3(2x + 3) (2x - 3)(2x + 3)

25. Jhannybean

\begin{align}12x^2+12x+3 &\rightarrow 4x^2+4x+1 \\&\rightarrow x^2+4x+4 \\&\rightarrow (x+2)(x+2) \\&\rightarrow \left(x+\frac{2}{4}\right)\left(x+\frac{2}{4}\right) \\&\rightarrow \left(x+\frac{1}{2}\right)\left(x+\frac{1}{2}\right) \\&\rightarrow \color{red}{(2x+1)(2x+1)}\end{align}

26. Jhannybean

For this method i simplify the quadratic by putting it in standard form $$ax^2+bx+c$$ typically where $$a=1$$ find the factors divide the factors by the leading coefficient we used to simplify our equation If the simplification of the factors does not give you an integer value but a fractional one, multiply the variable with the denominator of the fraction. You'll have your factorization

27. Nnesha

if there is a GCF better to take it out |dw:1444172023392:dw|

28. Nnesha

|dw:1444172039740:dw|

29. Nnesha

$12x^2+6x ---> 6x(2x+1)$ these are the mistakes :=)