Question

  Factorise  (x-3)^2 – 49​

Answer 1

Answer:

(x-3)^2 =49

(x-3) =√49

((x-3) =7

x =7+3

x =10

hope this is helpful to you

Answer 2

Question:

Factorise: (x-3)² - 49

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Solution:

We are given the expression (x-3)² - 49.

In order to factorise the provided expression, we will use the identity,

$\boxed {\sf {\pink {a^{2}-b^{2} = (a+b)(a-b)}}}$

Why will we use this identity?

We can see that (x-3)² and 49 (or 7²) are perfect squares, and they are in the form of a²-b².

(x-3)² - 49

(x-3)² - 7²

a² - b²

In the identity,

a = (x-3)

b = 7

So,

(x-3)² - (7)²

$\bigstar {\sf {\orange {Using\ the\ identity\ a^{2}-b^{2} = (a+b)(a-b)}}}$

$\implies \sf{(x-3+7) (x-3-7)}$

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Final answer:

Factorised form of (x-3)² - 49 is $\bf \red{(x-3+7) (x-3-7)}$.

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Steps:

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.