<PRE><B>Question 50472</B>
&lt;font size = 5&gt;&lt;b&gt;&lt;pre&gt;&lt;font color = &quot;darkmagenta&quot;&gt;The first seven cannot be factored, but the last
three can be:

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8)4x to the power of four + y to the power of four

4x&lt;sup&gt;4&lt;/sup&gt; + y&lt;sup&gt;4&lt;/sup&gt;

Add and subtract 4x&lt;sup&gt;2&lt;/sup&gt;y&lt;sup&gt;2&lt;/sup&gt;

4x&lt;sup&gt;4&lt;/sup&gt; + 4x&lt;sup&gt;2&lt;/sup&gt;y&lt;sup&gt;2&lt;/sup&gt; + y&lt;sup&gt;4&lt;/sup&gt; - 4x&lt;sup&gt;2&lt;/sup&gt;y&lt;sup&gt;2&lt;/sup&gt;

The first three terms can be factored as a perfect square, and
the last term is itself a perfect square.

(2x&lt;sup&gt;2&lt;/sup&gt; + y&lt;sup&gt;2&lt;/sup&gt;)&lt;sup&gt;2&lt;/sup&gt; - (2xy)&lt;sup&gt;2&lt;/sup&gt;

This is the difference of two perfect squares:

[(2x&lt;sup&gt;2&lt;/sup&gt; + y&lt;sup&gt;2&lt;/sup&gt;) - 2xy][(2x&lt;sup&gt;2&lt;/sup&gt; + y&lt;sup&gt;2&lt;/sup&gt;) + 2xy]

Get rid of unnecessary grouping symbols:

(2x&lt;sup&gt;2&lt;/sup&gt; + y&lt;sup&gt;2&lt;/sup&gt; - 2xy)(2x&lt;sup&gt;2&lt;/sup&gt; + y&lt;sup&gt;2&lt;/sup&gt; + 2xy)

Arrange in descending powers of x and ascending
powers of y

(2x&lt;sup&gt;2&lt;/sup&gt; - 2xy + y&lt;sup&gt;2&lt;/sup&gt;)(2x&lt;sup&gt;2&lt;/sup&gt; + 2xy + y&lt;sup&gt;2&lt;/sup&gt;)

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9)16x to the power of four z + 4z to the power of five

16x&lt;sup&gt;4&lt;/sup&gt;z + 4z

Factor out GCF 4z

4z{4x&lt;sup&gt;4&lt;/sup&gt; + 1}

Add and subtract 4x2 in the braces

4z{4x&lt;sup&gt;4&lt;/sup&gt; + 4x&lt;sup&gt;2&lt;/sup&gt; + 1 - 4x&lt;sup&gt;2&lt;/sup&gt;}

The first three terms in braces can be factored as a
perfect square, and the last term is itself a perfect 
square.

4z{(2x&lt;sup&gt;2&lt;/sup&gt; + 1)&lt;sup&gt;2&lt;/sup&gt; - (2x)&lt;sup&gt;2&lt;/sup&gt;}

The expression in braces is the difference of two 
perfect squares

4z{[(2x&lt;sup&gt;2&lt;/sup&gt; + 1) - (2x)][(2x&lt;sup&gt;2&lt;/sup&gt; + 1) + (2x)]

Get rid of unnecessary grouping symbols

4z(2x&lt;sup&gt;2&lt;/sup&gt; + 1 - 2x)(2x&lt;sup&gt;2&lt;/sup&gt; + 1 + 2x)

Arrange the expressions in parentheses in descending
order of x

4z(2x&lt;sup&gt;2&lt;/sup&gt; - 2x + 1)(2x&lt;sup&gt;2&lt;/sup&gt; + 2x + 1)

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10)10xz to the power of four + 40x

10xz&lt;sup&gt;4&lt;/sup&gt; + 40x

Factor out GCF 10x

10x{z&lt;sup&gt;4&lt;/sup&gt; + 4}

Add and subtract 4z&lt;sup&gt;2&lt;/sup&gt; in the braces

10x{z&lt;sup&gt;4&lt;/sup&gt; + 4z&lt;sup&gt;2&lt;/sup&gt; + 4 - 4z&lt;sup&gt;2&lt;/sup&gt;}

The first three terms in braces can be factored as a
perfect square, and the last term is itself a perfect 
square.

10x{(z&lt;sup&gt;2&lt;/sup&gt; + 2)&lt;sup&gt;2&lt;/sup&gt; - (2z)&lt;sup&gt;2&lt;/sup&gt;}

The expression in braces is the difference of two 
perfect squares

10x{[(z&lt;sup&gt;2&lt;/sup&gt; + 2) - (2z)][(z&lt;sup&gt;2&lt;/sup&gt; + 2) + (2z)]

Get rid of unnecessary grouping symbols

10x(z&lt;sup&gt;2&lt;/sup&gt; + 2 - 2z)(z&lt;sup&gt;2&lt;/sup&gt; + 2 + 2z)

Arrange the expressions in parentheses in descending
order of z

10x(z&lt;sup&gt;2&lt;/sup&gt; - 2z + 2)(z&lt;sup&gt;2&lt;/sup&gt; + 2z + 2)

Edwin&lt;/pre&gt;&lt;/font&gt;&lt;/b&gt;</PRE>