Question

What should be subtracted from


`{a}^(2) - 7ab \: + {3b}^(2)`
to get

`( - 4 {a}^(2) + 6ab \: + 3 {b}^(2) )`
?​

Answer 1

-5a²+13ab should be subtracted.

Step-by-step explanation:-

Based on the given conditions, formulate,

`→- {a}^(2) - 4 {a}^(2) + 13ab`

`→-({a}^(2) - 4 {a}^(2)) + 13ab`

Taking the coefficients or numbers, we get,

`→(- 1 - 4) {a}^(2) + 13ab`

`→ - 5 {a}^(2) + 13ab`

Answer 2

Given :

What should be subtracted from a² – 7ab + 3b² to get – 4a² + 6ab + 3b² ?

Solution :

Let the required expression to be subtracted be x

⇢ a² – 7ab + 3b² – x = – 4a² + 6ab + 3b²

⇢ a² – 7ab + 3b² – (– 4a² + 6ab + 3b²) = x

⇢ a² – 7ab + 3b² + 4a² – 6ab – 3b² = x

Combining the like terms :

⇢ a² + 4a² – 7ab – 6ab + 3b² – 3b² = x

⇢ 5a² – 13ab = x

⇢ x = 5a² – 13ab

Therefore,

5a² – 13ab should be subtracted from a² – 7ab + 3b² to get – 4a² + 6ab + 3b².