How do you factor #4x^3 + 32#?
1 Answer
Aug 25, 2016
Explanation:
First step is to take out a
#color(blue)"common factor"# of 4.
#rArr4x^3+32=4(x^3+8)........ (A)# Now,
#x^3+8 color(blue)" is a sum of cubes"# and in general is factorised as follows.
#color(red)(|bar(ul(color(white)(a/a)color(black)(a^3+b^3=(a+b)(a^2-ab+b^2))color(white)(a/a)|)))........ (B)# now,
#(x)^3=x^3" and " (2)^3=8rArra=x" and "b=2# substitute these values for a and b into (B)
#rArrx^3+8=(x+2)(x^2-2x+4)# substitute back into (A)
#rArr4x^3+32=4(x+2)(x^2-2x+4)#