Question

Subtract 7a^4-4a^2b^2+67a 4 −4a 2 b 2 +6 from 3a^4+2ab^2+113a 4 +2ab 2 +11.

Answer 1

`42a^4+4ab^2+8ab^b^2+5`

Explanation:

Subtract
`7a^4-4a^2b^2+67a^4 -4a^2b^2 +6` from
`3a^4+2ab^2+113a^4 +2ab^2 +11`

Lets arrange the terms in order and then subtract. when we subtract we change the sign of each term in second parenthesis

`(3a^4+2ab^2+113a^4 +2ab^2 +11)-(7a^4-4a^2b^2+67a^4 -4a^2b^2 +6)`

`3a^4+2ab^2+113a^4 +2ab^2 +11-7a^4+4a^2b^2-67a^4 +4a^2b^2 -6)`

Now we combine like terms

`3a^4 -7a^4+113a^4-67a^4= 42a^4`

`2ab^2+2ab^2= 4ab^2`

`+4a^2b^2+4a^2b^2=8a^2b^2`

`11-6=5`

The final expression is

`42a^4+4ab^2+8ab^b^2+5`

Answer 2

`34a^(4)+12a^(2)b^(2)+5`

Explanation:

The given equation is

`7a^(4)-4a^(2)b^(2)+67a^(4)-4a^(2)b^(2)+6` .................(i)

we have to subtract it from

`3a^(4)+2a^(2)b^(2)+113a^(4)+2a^(2)b^(2)+11` .................(ii)

First we will take the same terms of the equations in it and solve them

taking equation (i) and solving the similar terms

`7a^(4)-4a^(2)b^(2)+67a^(4)-4a^(2)b^(2)+6`

=
`84a^(4)-8a^(2)b^(2)+6` .......................................(iii)

taking equation (ii) and solving similar terms

`3a^(4)+2a^(2)b^(2)+113a^(4)+2a^(2)b^(2)+11`

=
`116a^(4)+4a^(2)b^(2)+11` ......................................(iv)

Now we have to subtract (iii) from (iv)

which will be

=
`116a^(4)+4a^(2)b^(2)+11`-
`(84a^(4)-8a^(2)b^(2)+6)`

=
`116a^(4)+4a^(2)b^(2)+11 - 84a^(4)+8a^(2)b^(2)-6`

adding and subtracting the similar terms will give us

=
`34a^(4)+12a^(2)b^(2)+5`

this is the required answer