- #1
alpha01
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[tex](y + 3)^3 + 8[/tex]
my attempt has led me to
(y+3)(y+3)(y+3+8)
but i doubt this is correct
my attempt has led me to
(y+3)(y+3)(y+3+8)
but i doubt this is correct
alpha01 said:expanding and simplify the (y+3)^3:
(y^2 + 6y + 9)(y + 3)
alpha01 said:(z+2)(z+2)(z+2)
kbaumen said:To solve this one, you should know this formula: a^3 + b^3 = (a + b)(a - ab + b). I hope that helps.
Feldoh said:How are you getting z = -6?
[tex]z^3\,+\,8\,=\,0[/tex]
[tex]z^3\,=\,-8[/tex]
[tex]z\,=\,(-8)^{1/3}[/tex]
alpha01 said:So, putting (y+3)^3 +8 in the form (a+b)(a^2 -ab+b^2):
[tex]((y+3)+2) ((y+3)^2 -2(y+3)+4)[/tex]
but i don't think this is completely factorized?
Gib Z said:I'm not trying to be rude, but from posts 1, 3 and 6 it seems to me you really need to go back and brush up on your algebra.
Gib Z said:I'm not trying to be rude, but from posts 1, 3 and 6 it seems to me you really need to go back and brush up on your algebra.
It certainly isn't correct because you can't take the "8" inside one factor. That 8 would now be multiplied by the other "(y+ 3)" terms and it isn't in the original form.alpha01 said:[tex](y + 3)^3 + 8[/tex]
my attempt has led me to
(y+3)(y+3)(y+3+8)
but i doubt this is correct
alpha01 said:So, putting (y+3)^3 +8 in the form (a+b)(a^2 -ab+b^2):
[tex]((y+3)+2) ((y+3)^2 -2(y+3)+4)[/tex]
but i don't think this is completely factorized?
Factorizing is the process of breaking down an expression into smaller parts that can be multiplied together to get the original expression. In this case, (y + 3)^3 + 8 can be factored into (y + 3)(y + 3)(y + 3) + 8.
The first step is to identify if there are any common factors that can be pulled out of the expression. In this case, there are no common factors between (y + 3)^3 and 8. Next, we can use the formula (a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3 to expand (y + 3)^3. This gives us (y^3 + 9y^2 + 27y + 27) + 8. Finally, we can combine like terms to get the final factorized form of (y + 3)(y^2 + 9y + 35).
No, (y + 3)^3 + 8 is already in its simplest factorized form. The expression cannot be broken down into smaller parts without changing its meaning.
Factorizing is used in various fields such as mathematics, physics, and engineering. It helps in simplifying complex expressions, solving equations, and finding the roots of polynomials. It is also used in simplifying problems in chemistry and economics.
One helpful tip is to always look for common factors first. If there are no common factors, try to use known formulas to expand the expression. It is also helpful to practice factoring different types of expressions to improve your skills.