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What is (x+4)^4 expanded

Guest Feb 15, 2017

Best Answer 

 #3
avatar+19653 
+10

What is (x+4)^4 expanded

 

\(\small{ \begin{array}{|rcll|} \hline (x+4)^4 &=& [(x+4)^2]^2 \quad &| \quad (x+4)^2 = x^2+8x+16 \\ &=& (x^2+8x+16)^2 \\ &=& [x^2+(8x+16)]^2 \\ &=& (x^2)^2 + 2\cdot x^2 \cdot (8x+16)+(8x+16)^2 \quad &| \quad (8x+16)^2 = (8x)^2+2\cdot 8x \cdot 16 + 16^2 \\ &=& (x^2)^2 + 2\cdot x^2 \cdot (8x+16)+(8x)^2+2\cdot 8x \cdot 16 + 16^2 \\ &=& x^4 + 2\cdot x^2 \cdot 8x +2\cdot x^2 \cdot 16 +64x^2+ 256x + 256 \\ &=& x^4 + 16 x^3 +32x^2 +64x^2+ 256x + 256 \\ &=& x^4 + 16\ x^3 +94x^2+ 256x + 256 \\ \hline \end{array} }\)

 

laugh

heureka  Feb 16, 2017
 #1
avatar+234 
0

(x+4)^4 is the same as (x+4)(x+4)(x+4)(x+4)

which can be further simplified to 4x+256

;)

HelpMeWithThisPlease  Feb 15, 2017
 #2
avatar+12560 
0

I just went to WolframAlpha :

 

ElectricPavlov  Feb 15, 2017
 #3
avatar+19653 
+10
Best Answer

What is (x+4)^4 expanded

 

\(\small{ \begin{array}{|rcll|} \hline (x+4)^4 &=& [(x+4)^2]^2 \quad &| \quad (x+4)^2 = x^2+8x+16 \\ &=& (x^2+8x+16)^2 \\ &=& [x^2+(8x+16)]^2 \\ &=& (x^2)^2 + 2\cdot x^2 \cdot (8x+16)+(8x+16)^2 \quad &| \quad (8x+16)^2 = (8x)^2+2\cdot 8x \cdot 16 + 16^2 \\ &=& (x^2)^2 + 2\cdot x^2 \cdot (8x+16)+(8x)^2+2\cdot 8x \cdot 16 + 16^2 \\ &=& x^4 + 2\cdot x^2 \cdot 8x +2\cdot x^2 \cdot 16 +64x^2+ 256x + 256 \\ &=& x^4 + 16 x^3 +32x^2 +64x^2+ 256x + 256 \\ &=& x^4 + 16\ x^3 +94x^2+ 256x + 256 \\ \hline \end{array} }\)

 

laugh

heureka  Feb 16, 2017

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