Question

factorise the following expression using identities. x^2+8x+16​

Answer 1

Answer:

(x−4)2

Explanation:

Given: x2−8x+16.

We find two numbers, say a and b, such that a+b=−8 and ab=16.

Mentally, I see that a=b=−4. Checking, (−4)+(−4)=−8,−4⋅−4=16.

Now, we split it into:

=x2+ax+bx+16

=x2−4x−4x+16

=x(x−4)−4(x−4)

=(x−4)(x−4)

=(x−4)2

Step-by-step explanation:

Answer 2

Answer:

⇒ ( x − 4 ) 2

Step-by-step explanation:

x 2 − 8 x + 16

⇒x 2 − ( 2 . 4 ⋅ x ) + 4 2

It’s in the form a 2 − 2 a b + b 2 = ( a − b ) 2

∴ ⇒ ( x − 4 )