Question

9xy^2-x^3........???​

Answer 1

Answer:

STEP

1

:

Equation at the end of step 1

32xy2 - x3

STEP

2

:

STEP

3

:

Pulling out like terms

3.1 Pull out like factors :

9xy2 - x3 = -x • (x2 - 9y2)

Trying to factor as a Difference of Squares:

3.2 Factoring: x2 - 9y2

Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =

A2 - AB + BA - B2 =

A2 - AB + AB - B2 =

A2 - B2

Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : 9 is the square of 3

Check : x2 is the square of x1

Check : y2 is the square of y1

Factorization is : (x + 3y) • (x - 3y)

Final result :

-x • (x + 3y) • (x - 3y)

Answer 2

we have,

$\tt♔9 x{y}^{2} - {x}^{3}$

$\tt➻9 x{y}^{2} - {x}^{3}$

$\tt➻ \orange{factor \: out} \: x \: from \: the \: expression.$

$\huge⥿⥿⥿⥿$

$\tt➻ \red{ x(9 {y}^{2} - {x}^{2} )}$

$\tt➻ x \red{((3 {y)}^{2} - ({x})^{2} )}$

$\tt➻ using \: {a}^{2} - {b}^{2} = (a - b)(a + b), \\ \tt \orange{factor} \: the \: expression.$

$\huge⥿⥿⥿⥿$

$\tt➻ x \red{(3y - x)(3y + x)}$

SOLUTION:-

$\tt↬ x(3y - x)(3y + x)$