Question

if a = x^2+xy-6, b =6xy -2x^2+1, c = 3x^2+7-3xy , find a+b-c​

Answer 1

Step-by-step explanation:

STEP1:

y Simplify — x

Equation at the end of step1:

(y2) (y2) y (((((x2)-(————•(x2)))+6xy)+((3•————)•x))+(5•—))-y 3 5 x

STEP 2 :

y2 Simplify —— 5

Equation at the end of step2:

(y2) y2 5y (((((x2)-(————•(x2)))+6xy)+((3•——)•x))+——)-y 3 5 x

STEP 3 :

y2 Simplify —— 3

Equation at the end of step3:

y2 3xy2 5y (((((x2)-(——•x2))+6xy)+————)+——)-y 3 5 x

STEP4:Equation at the end of step 4

x2y2 3xy2 5y (((((x2)-————)+6xy)+————)+——)-y 3 5 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  3  as the denominator :

x2 x2 • 3 x2 = —— = —————— 1 3

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

Adding fractions that have a common denominator :

 5.2       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:

x2 • 3 - (x2y2) 3x2 - x2y2 ——————————————— = —————————— 3 3

Equation at the end of step5:

(3x2 - x2y2) 3xy2 5y (((———————————— + 6xy) + ————) + ——) - y 3 5 x

STEP6:Rewriting the whole as an Equivalent Fraction

 6.1   Adding a whole to a fraction

Rewrite the whole as a fraction using  3  as the denominator :

6xy 6xy • 3 6xy = ——— = ——————— 1 3

STEP7:Pulling out like terms

 7.1     Pull out like factors :

   3x2 - x2y2  =   -x2 • (y2 - 3) 

Trying to factor as a Difference of Squares:

 7.2      Factoring:  y2 - 3 

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 : 3 is not a square !!