Question

a² - ab - 20b² factorisation​

Answer 1

Proper Question: Write the factorisation of a² - ab - 20b².

Answer: On the factorisation of the given expression a² - ab - 20b² we get (a + 4b) (a - 5b).

Given:

The given expression is a² - ab - 20b².

To Find:

The factorisation of a² - ab - 20b².

Solution:

→ The given expression a² - ab - 20b² is a polynomial of degree 2, therefore it must have 2 factors.

→ We would factorise the given expression by splitting the middle term:

• The product of the first term and the last term is equal to -20a²b².
• Therefore we will split the middle term into two terms such that their product is equal to -20a²b².
• We would split -ab into -5ab and 4ab.

                                               ∵ a² - ab - 20b²

                                           ∴ a² - 5ab + 4ab - 20b²

                                          ∴ a (a - 5b) + 4b (a - 5b)

                                                ∴ (a + 4b) (a - 5b)

→ Therefore on factorisation of (a² - ab - 20b²) we get (a + 4b) (a - 5b).

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