Question

factorize 4x²+20xy+25y²​

Answer 1

Answer:

( 2x + 5y )^2

Step-by-step explanation:

Explanation:

Use the formula for the square of a binomial: (a+b)2=a2+2ab+b2.

Both 4 and 25, the coefficient of x2 and y2, are perfect squares. This makes us think that the whole expression could be a perfect square: 4 is 22, and 25 is 52. So, our claim is that

4x2−20xy+25y2 is (2x−5y)2. Is it true? The only term to verify is −20xy, and it is indeed twice the product of 2x and −5y. So, the conjecture was right.

Answer 2

Answer:

= (2x - 5y)²

Step-by-step explanation:

$\huge\colorbox{yellow}{Solution\:-}$

${4x}^{2} - 20xy + {25y}^{2}$

${4x}^{2} - 10xy - 10xy + {25y}^{2}$

$2x(2x - 5y) - 5y(2x - 5y)$

$= (2x - 5y)(2x - 5y)$

$\boxed{\pink{ = > (2x - 5y)^{2} }}$

$\huge\colorbox{yellow}{Thank\:You}$