Question

Please list and tell me all the factors of question 11

Answer 1

Given:

`1-49a^2`

Required:

We need to factorize the given expression.

Step-by-step explanation:

`Use\text{ 1=1}^2\text{ and }49=7^2.`

`1-49a^2=1^2-7^2a^2`
`Use\text{ }7^2a^2=(7a)^2.`

`1-49a^2=1^2-(7a)^2`

The given expression is a difference of perfect sqaure because 1 is the perfect sqaure and 49 is also the perfect square of 7.

We know that a multiple of a perfect sqaure is also a perfect square.

`49a^2\text{ is a perfect square.}`

We get

`1^2-(7a)^2,`

Use the structure of the difference of perfect squares to factorize the given expression.

`(a^2-b^2)=(a-b)(a+b)`

Substitute a =1 and b =7a in the formula.

`1^2-(7a)^2=(1-7a)(1+7a)`

`1-49a^2=(1-7a)(1+7a)`

The number of factors = 2

Final answer:

The given expression is a difference of perfect sqaure because 1 is the perfect sqaure and 49 is also the perfect square of 7.

We know that a multiple of a perfect sqaure is also a perfect square.

`1-49a^2=(1-7a)(1+7a)`

The number of factors = 2