Question

find the factors.i need with perfect explanation
$3x {}^{2} + 6x {}^{2}y + 9x y {}^{2}$

Answer 1

Hey mate,

x3+6x2y-9xy2

Final result :

x • (x2 + 6xy - 9y2)

Step by step solution :

Step 1 :

Equation at the end of step 1 :

((x3)+((6•(x2))•y))-32xy2

Step 2 :

Equation at the end of step 2 :

((x3) + ((2•3x2) • y)) - 32xy2

Step 3 :

Step 4 :

Pulling out like terms :

4.1 Pull out like factors :

x3 + 6x2y - 9xy2 = x • (x2 + 6xy - 9y2)

Trying to factor a multi variable polynomial :

4.2 Factoring x2 + 6xy - 9y2

Try to factor this multi-variable trinomial using trial and error

Factorization fails

Final result :

x • (x2 + 6xy - 9y2)

Hope it will help you.

✨It's M.S.V.

Answer 2

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$\sf{\underline{Simplifying}}$


3x2 + 6x2y + 9xy2 = 0


$\sf{\underline{Record\:the\:terms:}}$


9xy2 + 3x2 + 6x2y = 0


$\sf{\underline{Solving:}}$


9xy2 + 3x2 + 6x2y = 0


Solving for variable 'x'.


Factor out the Greatest Common Factor (GCF), '3x'.

3x(3y2 + x + 2xy) = 0

Ignore the factor 3.


$\sf{\underline{Subproblem-1}}$

Set the factor 'x' equal to zero and attempt to solve:

Simplifying x = 0

Solving x = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying x = 0


$\sf{\underline{Subproblem-2}}$

Set the factor '(3y2 + x + 2xy)' equal to zero and attempt to solve:

Simplifying 3y2 + x + 2xy = 0


$\sf{\underline{Record\:the\:terms:}}$

x + 2xy + 3y2 = 0


$\sf{\underline{Solving:}}$

x + 2xy + 3y2 = 0

Move all terms containing x to the left, all other terms to the right.

Add '-3y2' to each side of the equation.

x + 2xy + 3y2 + -3y2 = 0 + -3y2


$\sf{\underline{Combine\:like\:terms:}}$

3y2 + -3y2 = 0

x + 2xy + 0 = 0 + -3y2

x + 2xy = 0 + -3y2


$\sf{\underline{Remove\:the\:zero:}}$

x + 2xy = -3y2


The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.


$\sf{\underline{Solution:}}$

x = {0}


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