Question

factorise:m^2+m-72
Answer me i will mark ad brilliant!!!!​

Answer 1

Answer:

2

+

−

7

2

m^{2}+m-72

m2+m−72

Grouping

1

Use the sum-product pattern

2

+

−

7

2

m^{2}+{\color{#c92786}{m}}-72

m2+m−72

2

+

9

−

8

−

7

2

m^{2}+{\color{#c92786}{9m}}{\color{#c92786}{-8m}}-72

m2+9m−8m−72

2

Common factor from the two pairs

3

Rewrite in factored form

Solution

(

−

8

)

(

+

9

)

Answer 2

Question:

Factorise: m²+m -72

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Solution:

Here, to factorise this expression, we will use splitting the middle term method.

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Steps to split the middle term:

☆ Find the product of the first and the last term.

$\sf \pink {1m²\times 72=72}$ We can ignore the variable.

☆ Find the factors of the product so obtained.

$\sf \pink {1 \times 72}$

$\sf \pink {2 \times 36}$

$\sf \pink {3 \times 24}$

$\sf \pink {4 \times 18}$

$\sf \pink {6 \times 12}$

$\sf \pink {8 \times 9}$

.

.

.

☆ Find the two numbers whose product is equal to that of the first and last term and whose sum or difference is equal to that of the middle term.

$\sf \pink {9 \times 8=72\ and\ 9-8=1}$

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Solution continued:

m²+m -72

m²+(9-8)m -72

m²+9m - 8m -72

On regrouping the terms,

(m²+9m) - (8m -72)

Take out common from each group,

m(m+9) - 8(m+9)

$\boxed {\sf {\red {(m-8) (m+9)}}}$

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Final answer:

The factorised form of m²+m -72 is

(m-8) (m+9).

__________________

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