Question

what term should be added in (x)2-??+16 to make a perfect square?​

Answer 1

(m + n)² = m² + 2mn + n² and (m - n)² = m² - 2mn + n².  

1. 4a² = (2a)²  

28a = 2(2a)7  

∴ The answer is 7² = 49.  

4a² + 28a + 49 = (2a + 7)².  

2. 16 = 4²

8y = 2(4)y

∴ The answer is y².  

y² + 8y + 16 = (y + 4)².  

3. [This question has 2 explanations but 1 answer] a² = (a)²

-2a = 2(a)-1  

∴ The answer is (-1)² = 1.  

a² - 2a + 1 = (a - 1)².  

OR

a² = (-a)²  

-2a = 2(-a)1

∴ The answer is 1² = 1.  

a² - 2a + 1 = (-a + 1)² = (1 - a)².  

4. [This question has 2 explanations but 1 answer] 9 = (3)²  

-6x = 2(3)-x

∴ The answer is (-x)² = x²

x² - 6x + 9 = (-x + 3)² = (3 - x)².  

OR  

9 = (-3)²  

-6x = 2(-3)x  

∴ The answer is x².  

x² - 6x + 9 = (x - 3)².  

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