Question 59383
Factor
{{{64w^3+8x^3}}}
The formula for factoring the sum of cubes is {{{highlight(a^3+b^3=(a+b)(a^2-ab+b^2))}}}
{{{8(8w^3+x^3)}}}  Factor out the GCF
{{{8((2w)^3+(x)^3)}}}  a=2w and b=x
{{{8(2w+x)((2w)^2-(2w)(x)+x^2)}}}
{{{highlight(8(2w+x)(4w^2-2wx+x^2))}}}



Solve
{{{2x^2-11x+13=1}}}
{{{2x^2-11x+13-1=1-1}}} set the problem = to 0.
{{{2x^2-11x+12=0}}}  Factor.  Replace the middle term with 2 terms that multiply to give you 2*12x^2=24x^2, and add together to give you -11x.  (-3x*-8x=-24x^2 and -3x+-8x=-11x)
{{{2x^2-3x-8x+12=0}}}  group the first 2 and last two terms.
{{{(2x^2-3x)+(-8x+12)=0}}}  Factor the GCF out of each group
{{{x(2x-3)-4(2x-3)=0}}}   Factor out the 2x-3
{{{(x-4)(2x-3)=0}}}  Set each parenthesis equal to 0 and solve for x.
x-4=0  and 2x-3=0
x-4+4=0+4 and 2x-3+3=0+3
x=4 and 2x=3
x=4 and 2x/2=3/2
x=4 and x=3/2
:
Happy Calculating!!!