Question

11. Factorise each of the following expressions completely: a² + 3ab-4b²​

Answer 1

a²+3ab-4b²=

(a−b)(a+4b)

Explanation:

Answer 2

`$$(a - b)(a + 4b)$$.`

Explanation:

The given expression is a quadratic expression of the form

`$$ax^2 + bx + c$$.`

To factorize the expression
`$$a² + 3ab - 4b²$$`, we need to find two numbers that add up to 3 (the coefficient of the middle term) and multiply to -4 (the coefficient of the last term).

The numbers that satisfy these conditions are 4 and -1. Therefore, we can write the middle term as
`$$4ab - ab$$`

So, the expression becomes
`$$a² + 4ab - ab - 4b²$$`. Now, we can factor by grouping:

`$$a² + 4ab - ab - 4b² = a(a + 4b) - b(a + 4b) = (a - b)(a + 4b)$$`

So, the factorization of the given expression
`$$a² + 3ab - 4b²$$` is
`$$(a - b)(a + 4b)$$.`

Hope this helps! :)