How do you factor: #y= 32x^3 - 4 #?
2 Answers
Explanation:
Recall:
Here we go.
By factoring out
By rewriting a bit,
By applying the formula at the top with
By cleaning up a bit,
I hope that this was clear.
Explanation:
The first step is to factor out
#color(blue)"common factor"# of 4
#rArry=4(8x^3-1)to(1)# now
#8x^3-1# is a#color(blue)"difference of cubes"# and factorises in general as.
#color(red)(bar(ul(|color(white)(2/2)color(black)(a^3-b^3=(a-b)(a^2+ab+b^2))color(white)(2/2)|)))#
#8x^3=(2x)^3" and " 1^3=1#
#"using " a=2x" and " b=1#
#rArr8x^3-1=(2x-1)(4x^2+2x+1)#
#"going back to " (1)#
#rArry=4(2x-1)(4x^2+2x+1)#