Question

4 po
Qı: A school has 3x^3 - 11x^2y + 11xy^2 - 2y^3 students and x - 2y buses, if all the
children have to be taken on a picnic, how many children should be allocated to each
bus?​

Answer 1

Answer:

Simplify ——

x

Equation at the end of step

1

:

y3

((((3•(x3))-((11•(x2))•y))+(11x•(y2)))-(2•——))-2y

x

STEP

2

:

Equation at the end of step

2

:

2y3

((((3•(x3))-((11•(x2))•y))+11xy2)-———)-2y

x

STEP

3

:

Equation at the end of step

3

:

2y3

((((3•(x3))-(11x2•y))+11xy2)-———)-2y

x

STEP

4

:

Equation at the end of step

4

:

2y3

(((3x3 - 11x2y) + 11xy2) - ———) - 2y

x

STEP

5

:

Rewriting the whole as an Equivalent Fraction

5.1 Subtracting a fraction from a whole

Rewrite the whole as a fraction using x as the denominator :

3x3 - 11x2y + 11xy2 (3x3 - 11x2y + 11xy2) • x

3x3 - 11x2y + 11xy2 = ——————————————————— = —————————————————————————

1 x

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

STEP

6

:

Pulling out like terms

6.1 Pull out like factors :

3x3 - 11x2y + 11xy2 = x • (3x2 - 11xy + 11y2)

Trying to factor a multi variable polynomial :

6.2 Factoring 3x2 - 11xy + 11y2

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

Factorization fails

Adding fractions that have a common denominator :

6.3 Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

x • (3x2-11xy+11y2) • x - (2y3) 3x4 - 11x3y + 11x2y2 - 2y3

——————————————————————————————— = ——————————————————————————

x x

Equation at the end of step

6

:

(3x4 - 11x3y + 11x2y2 - 2y3)

———————————————————————————— - 2y

x

STEP

7

:

Rewriting the whole as an Equivalent Fraction :

7.1 Subtracting a whole from a fraction

Rewrite the whole as a fraction using x as the denominator :

2y 2y • x

2y = —— = ——————

1 x

Checking for a perfect cube :

7.2 3x4 - 11x3y + 11x2y2 - 2y3 is not a perfect cube

Adding fractions that have a common denominator :

7.3 Adding up the two equivalent fractions

(3x4-11x3y+11x2y2-2y3) - (2y • x) 3x4 - 11x3y + 11x2y2 - 2xy - 2y3

————————————————————————————————— = ————————————————————————————————

x x

Final result :

3x4 - 11x3y + 11x2y2 - 2xy - 2y3

————————————————————————————————

x

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