Question

what term should be added to each of the following expressions to make it a perfect square ---

1. 4a^2+28a

2. 16+8y

3. a^2-2a

4. 9-6x

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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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Answer 2

Step-by-step explanation:

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