How do you know if 4x2−20x+25 is a perfect square trinomial and how do you factor it?
Answers
Answer:
Step-by-step explanation:
Answer:
4x^2 - 20x + 25 is a perfect square trinomial of ( 2x - 5 ).
Step-by-step explanation:
We can say that 4x^2 - 20x + 25 is a perfect square trinomial if it can be expressed in the form of ( a + b )^2.
In order to make them in this form, we have to factorize 4x^2 - 20x + 25.
We can factorize 4x^2 - 20x + 25 by using different different methods, here, two easy methods are given : -
Method 1 to factorize the equation :
= > 4x^2 - 20x + 25
= > ( 2x )^2 - 2( 5 × 2x ) + 5^2
From the properties of factorization : -
- a^2 - 2ab + b^2 = ( a - b )^2
= > ( 2x - 5 )^2
Method 2 to factorize the equation :
= > 4x^2 - 20x + 25
= > 4x^2 - ( 10 + 10 ) x + 25
= > 4x^2 - 10x - 10x + 25
= > 2x( 2x - 5 ) - 5( 2x - 5 )
= > ( 2x - 5 )( 2x - 5 )
= > ( 2x - 5 )^2
Hence the required factorized form of 4x^2 - 20x + 25 is ( 2x - 5 )^2.