Question

Find the value of (49x^2 - 70xy + 25y^2) if x = 5 and y = 7​

Answer 1

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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Answer 2

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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