Question 328850
<pre><font size = 4 color = "indigo"><b>
a.   {{{40x^3 - 64x^2y}}}

The largest whole number that will divide into both {{{40}}} and {{{64}}} is {{{8}}}.
So we can take out an {{{8}}}.

The largest power of x that will divide into both {{{x^3}}} and {{{x^2}}}
is {{{x^2}}}.

So we can take out {{{8x^2}}}

{{{8x^2(5x-8y)}}}


b.   {{{13-14y + y^2}}}

Write it in descending order:

{{{y^2}}}{{{""-""}}}{{{14y}}}{{{red(""+"")}}}{{{13}}}

Think of two positive integers which multiply to give 13,
and when <font color="red">added</font> give 14. 

<font size = 1>[If the red sign had been - I would have said "subtracted"]</font>

They are 13 and 1

Write this

(x   13)(x   1)

{{{y^2}}}{{{green(""-"")}}}{{{14y}}}{{{red(""+"")}}}{{{13}}}

Since the <font color = "green">green</font> sign is -, put a minus before the large of those
two numbers which is 13:

(x - 13)(x   1)

Since the red sign is negative put the OPPOSITE sign before the 1
that you put before the 13.

(x - 13)(x + 1)

<font size = 1>[If the red sign had been + I would have said "SAME"]</font>



c.   {{{9x^2- 30x + 25}}}

This is a special case where the first term and the last term are both
perfect squares.  the {{{9x^2}}} has square root {{{3x}}} and the {{{25}}}
has square root {{{5}}}.  Multiply these square roots together, getting {{{15x}}},
and then double that, getting {{{30x}}}.  Since this is the absolute value
of the middle term, the trinomial is a perfect square, so write

(3x   5)²

and the sign that goes between them is the same sign as the middle term:

(3x - 5)²

Edwin</pre>