Question

What is the factored form of the following expression? 25x^2 + 70x+ 49​

Answer 1

(5x + 7)2.

The expression is in the form a2x2 + 2abx + b2, where a = 5 and b = 7.

Thus, it can be factored as a perfect square trinomial.

Answer 2

( 5x + 7 ) ²

Explanation:

25 x ² + 70 x + 49

Identity Used

• (a + b) ² = a ² + 2 ab + b ²

= 25 x ² + 35 x + 35 x + 49

= 5 x ( 5x + 7 ) + 7 ( 5 x + 7)

= ( 5x + 7 )

More to know about Algebraic Identities :-

• ➛ (a + b)² = a² + 2ab + b²
• ➛ (a - b)² = a² - 2ab + b²
• ➛ a² - b² = (a +b) (a-b)
• ➛ (x + a) (x + b) = x² + (a + b) x + ab
• ➛ (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ac
• ➛ (a + b)³ = a³ + b³ + 3ab (a + b)
• ➛ (a - b)³ = a³ - b³ - 3ab (a + b)
• ➛ a³ + b³ + c³ = 3abc (If a + b + c = 0)
• ➛ a² + b² + c² = (a + b + c)² - 2 (ab + bc + ca)