Find the value of (49x^2 - 70xy + 25y^2) if x = 5 and y = 7
Answers
Given
- 49x² - 70xy + 25y²
- x = 5
- y = 7
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To Find
- Value of the expression
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Solution
There are two methods to solve this. Let's look into both of them -:
Method 1
Step 1: Substitute the value of variables.
⇒ 49x² - 70xy + 25y²
⇒ 49 (5)² - 70 (5)(7) + 25 (7)²
Step 2: Simplify the expression.
⇒ 49 (5)² - 70 (5)(7) + 25 (7)²
⇒ 49 × 25 - 2450 + 25 × 49
⇒ 1225 - 2450 + 1225
⇒ 2450 - 2450
⇒ 0
∴ 49x² - 70xy + 25y² = 0 when x = 5 and y = 7.
Method 2
Step 1: Simplify using the algebraic identity.
Identity → a² - 2ab + b² = (a - b)²
⇒ 49x² - 70xy + 25y²
⇒ (7x)² - 2(7x)(5y) + (5y)²
⇒ (7x - 5y)²
Step 2: Substitute the value of the variables.
⇒ (7x - 5y)²
⇒ [7(5) - 5(7)]²
Step 3: Simplify the expression.
⇒ [35 - 35]²
⇒ (0)²
⇒ 0
∴ 49x² - 70xy + 25y² = 0 when x = 5 and y = 7.
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Step-by-step explanation:
49×(5)^2-70(5)(7) + 25(7)^2
49×25 - 70×35 +25×49
1225 - 2450 + 1225
2450 - 2450
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