Question

factorise p^2+5pq+36q^2 Pleasee​

Answer 1

Correct question:

Factorise: $p^{2}+5pq+36q^{2}$

☆_____________________☆

Solution:

In order to factorise a given expression, follow these steps:

• Check if you can take out common factor from all the terms.

• Regrouping the terms.

• Using identity (a+b)² = a²+ 2ab + b²

• Using identity (a-b)² = a²- 2ab + b²

• Using identity a²-b² = (a+b) (a-b)

• Splitting the middle term.

☆_____________________☆

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

☆_____________________☆

Steps to split the middle term:

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

$\sf \red {1p \times 36q = 36}$ (We can ignore the variable)

☆ Find the factors of the product so obtained.

$\sf \red {1 \times 36}$

$\sf \red {2 \times 18}$

$\sf \red {3 \times 12}$  

$\sf \red {4 \times 9}$

.

.

.

☆ 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.

$\sf \red {9 \times 4=36\ and\ 9-4=5}$

☆_____________________☆

Solution continued:

$p^{2}+5pq+36q^{2}$

p²+ (9-4)pq +36q²

p²+ 9pq - 4pq + 36q²

Now, group the terms,

(p²+ 9pq) - (4pq + 36q²)

Take out common from each group,

p(p+9q) - 4q(p+9q)

Hence,

(p-4q) (p+9q)

☆_____________________☆

Final answer:

$\boxed {\sf {\blue {Factorised\ form\ of\ p^{2}+5pq+36q^{2}\ is\ (p-4q) (p+9q)}}}$

☆_____________________☆

See similar questions:

• https://brainly.in/question/31173354
• https://brainly.in/question/31110894
• https://brainly.in/question/30607594

Answer 2

Step-by-step explanation:

p²+5pq+36q²

=p²+9pq-4pq+36q²

=p(p+9q)-4q(p+9q)

=(p-4q)(p+9q)

hope it'll help you make it brainliest answer please and follow me