Question

I will fan and medal
can you please help mw with the steps

Part A: Factor 3x^2y^2 − 2xy^2 − 8y^2. Show your work. (4 points)

Part B: Factor x^2 + 10x + 25. Show your work. (3 points)

Part C: Factor x^2 − 36. Show your work. (3 points)

these are my answers
part a: y^2=(3x+4)(x-2)
part b: (x+5)(x+5)
part c: (x+6)(x-6)

Answer 1

so....have you done any factoring? have you covered factoring?

Answer 2

yes I have

Answer 3

I can check my answer using the FOIL method I just don't know the steps to factoring if that makes sense @jdoe0001

Answer 4

ok
well.. let's start backwards

any ideas on say C) since is very simple \(\bf x^2-36\) ?

Answer 5

are the answers I put at the bottom of my question right @jdoe0001

Answer 6

hmm ok
well, those are given, but anyhow

\(\bf x^2-36\qquad {\color{brown}{ 6^2=36}}\qquad thus\implies x^2-6^2
\\ \quad \\
--------------------------\\
\textit{difference of squares}
\\ \quad \\
(a-b)(a+b) = a^2-b^2\qquad \qquad
a^2-b^2 = (a-b)(a+b)\\
--------------------------------------\\
x^2-6^2\implies (x-6)(x+6)\)

Answer 7

okay so I would explain this one by saying the square root of 36 is 6

Answer 8

yes, or that 36 is the square of 6
and thus it makes it a difference of squares

Answer 9

so that is showing work on factoring?

Answer 10

for C), yes

Answer 11

B) is also simple
if we factor 25, we get 5, 5, 1 5*5*1 = 25
if we "multiply" then 5*5 we get the last term
if we "add" 5+5, we get the middle term

thus \(\begin{array}{cccllll}
x^2&+10&+25\\
&\uparrow &\uparrow \\
&5+5&5\cdot 5
\end{array}\implies (x+5)(x+5)\)

Answer 12

okay so if I were to explain it, it would be in order to factor x^2+10x+25 you pull out the GCF which in this case is 5 and simplify to (x+5)(x+5)

Answer 13

well... 5 is not the GCF, notice \(x^2\) doesn't have a 5

you'd factor out the last term, the constant one
and from a combination of two of its factors
you ought to get the middle term

Answer 14

so from the original problem of x^2+10x+25 you would factor the 10 and 25 and that's is supposed to be explaining the steps of how you get this answer?

Answer 15

hmm
well... you said you have already covered factoring
so...... you should recall that you need to factor out the constant
to get the values for the binomials