Question

Fill in the two blanks



(3a^3 - 5b^3) + __ a^3+__ b^3 = ( a^3 + b^3)

Answer 1

3a^3-5b^3+xa^3+yb^3=1a^3+1b^3

replace a^3 with z

replace b^3 with v (to make it easier to see)

3z-5v+xz+yv=z+v

3z+xz+yv-5v=1z+v

the terms match them

3z+xz=1z

divide both sides by z

3+x=1

minus 3

x=-2

yv-5v=1v

dividie both sides by v

y-5=1

addd 5 to both sides

y=6

(3a^3-5b^3)+ -2 a^3 +6 b^3=(a^3+b^3)

Answer 2

The final answer is

3a^3 - 5b^3 - 2a^3 + 6b^3 = a^3 + b^3

Explanation:

It is given that an expression

(3a^3 - 5b^3) + __ a^3+__ b^3 = ( a^3 + b^3)

To find the missing numbers

From the given expression we can write,

3a^3 - 5b^3 + __ a^3+__ b^3 = a^3 + b^3

Compare LHS and RHS

3a^3 + __a^3 = a^3

__a^3 = a^3 - 3a^3

__a^3 = -2a^3

-5b^3 + __b^3 = b^3

__b^3 = b^3 + 5b^3

__b^3 = 6b^3

Therefore the final answer is

3a^3 - 5b^3 - 2a^3 + 6b^3 = a^3 + b^3