Mathematics, 25.07.2019 14:30 jinaicoeurvictp4ogwg
What identity can be used to rewrite the expression 8x^3+243
Answers: 1
. Notice that we can express 8 as a cube:Â 
, so we can rewrite our first term as 
. Since our second term does not have a exact cubic root, we must rewrite as ![\sqrt[3]{243} ^{3}](/tpl/images/0131/4422/a27a9.png)
. Now we have 
and ![b= \sqrt[3]{243}](/tpl/images/0131/4422/1a1fc.png)
, so lets use the sum of cube identity to rewrite our expression:![(2x)^3+ \sqrt[3]{243} ^3=(2x+ \sqrt[3]{243} )((2x)^2-2x \sqrt[3]{243} + \sqrt[3]{243} ^2](/tpl/images/0131/4422/b7517.png)
![(2x)^3+ \sqrt[3]{243} ^3=(2x+ 3\sqrt[3]{3^2} )((4x^2-6x \sqrt[3]{3^2} +27 \sqrt[3]{3} )](/tpl/images/0131/4422/d0f21.png)
![(2x)^3+ \sqrt[3]{243} ^3=(2x+ 3\sqrt[3]{9} )((4x^2-6x \sqrt[3]{9} +27 \sqrt[3]{3} )](/tpl/images/0131/4422/f35d8.png)
![(2x+ 3\sqrt[3]{9} )((4x^2-6x \sqrt[3]{9} +27 \sqrt[3]{3} )](/tpl/images/0131/4422/8b131.png)
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What identity can be used to rewrite the expression 8x^3+243...
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