Question #34bd6

2 Answers
sankarankalyanam
Oct 22, 2017

#(3x)^4(9x^2 + 625)#

Can also be written as

#(3x)^4)*((3x)^2 + 5^4)#

Explanation:

# (-3x)^6 + (15x)^4#

#( (-3)^6 * x^6) + ((15)^4 * x^4)#

#(3^6 * x^6) + (3^4 * 5^4 * x^4) as (-3)^6 = 3^6#

Taking common terms out,
#= (3^4* x^4) * ((3^2 * x^2) + 5^4)#

# = (3x)^4 (9x^2 + 625)#

Tony B
Oct 22, 2017

#81x^4(9x^2+625)#

Explanation:

First lets try a test using easy numbers to see if the numbers behave as hoped:

Consider the test
#(4x)^2 =16x^2-> (2x xx2)^2 = (2x)^2xx2^2 = 4x^2xx4=16x^2#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Answering the question")#

Using the above approach lets 'force' common factors to occur.
Note that #(-3)xx(-5)=+15#

Given: #(-3x)^6+(15x)^4#

write as: #[-3x]^6+[-3x xx(-5)]^4#

This is the same as:

#color(white)("d")[(-3x)^4(-3x)^2] + [(-3x)^4(-5)^4]#

Factoring out #(-3x)^4[(-3x)^2+(-5)^4]#

Note that #(-3x)^n# where #n# is even gives a positive value
So #(-3x)^4=(+3x)^4#. Also #(-5)^4# is even.

#(3x)^4[9x^2+ 5^4] #

#81x^4(9x^2+625)#

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