Question

factorise 1)4m square- 9mn-9n square who will solve this I will give like you and I will follow you and I will make you branilist​

Answer 1

Given:

• Need to factorise ${4m}^{2} - 9mn - 9n$

Solution:

Try to find common factors:

$4 {m}^{2} - 9mn - 9n = 0 \\ \implies \: 4 {m}^{2} - 12mn + 3mn - 9$

$\implies \: 4m(m - 3n) + 3n(m - 3n)$

$\red{\bold{\boxed{\implies \: (4m + 3n)(m - 3n)}}}$

━━━━━━━━━━━━━━━━━━

Knowledge cell:

How to find the factors?

With the quadratic equation in the form:

$\purple{\bold{P {(variable)}^{2} + Q(variable) + R}}$

Where P, Q and R are constants.

• Find two numbers that multiply to give P×R  and add/subtract to give Q

• Rewrite the middle term (Q×variable) in terms of those two numbers [either by adding or by subtracting]

• Watch which is common factor the first two and last two terms separately

• Now see, interestingly, our two new terms should have a clearly visible common factor.

• Thus we are successfully done with factorising!

Answer 2

Step-by-step explanation:

Given:

Need to factorise {4m}^{2} - 9mn - 9n4m

2

−9mn−9n

Solution:

Try to find common factors:

\begin{gathered}4 {m}^{2} - 9mn - 9n = 0 \\ \implies \: 4 {m}^{2} - 12mn + 3mn - 9\end{gathered}

4m

2

−9mn−9n=0

⟹4m

2

−12mn+3mn−9

\implies \: 4m(m - 3n) + 3n(m - 3n)⟹4m(m−3n)+3n(m−3n)

\red{\bold{\boxed{\implies \: (4m + 3n)(m - 3n)}}}

⟹(4m+3n)(m−3n)

━━━━━━━━━━━━━━━━━━

Knowledge cell:

How to find the factors?

With the quadratic equation in the form:

\purple{\bold{P {(variable)}^{2} + Q(variable) + R}}P(variable)

2

+Q(variable)+R

Where P, Q and R are constants.

Find two numbers that multiply to give P×R and add/subtract to give Q

Rewrite the middle term (Q×variable) in terms of those two numbers [either by adding or by subtracting]

Watch which is common factor the first two and last two terms separately

Now see, interestingly, our two new terms should have a clearly visible common factor.

Thus we are successfully done with factorising!