what time should be added to each of the following expressions for making it perfect square? 36a²+49b
Answers
Answer:
Step-by-step explanation:
(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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