75 × 75 – 2 × 75 × 25 + 25 × 25 is equal to:
2500
To solve the given expression 75 × 75 – 2 × 75 × 25 + 25 × 25, we can simplify it by recognizing it as a perfect square trinomial. The expression is of the form (a – b)2, where a = 75 and b = 25. The square of a binomial is given by: (a – b)2 = a2 – 2ab + b2.
Let's compare the terms:
- a2 = 75 × 75
- 2ab = 2 × 75 × 25
- b2 = 25 × 25
Substituting these into the expression:
- a2: 75 × 75 = 5625
- 2ab: 2 × 75 × 25 = 3750
- b2: 25 × 25 = 625
Thus, the expression simplifies to:
5625 – 3750 + 625
Calculating step-by-step:
- 5625 – 3750 = 1875
- 1875 + 625 = 2500
Hence, the value of the expression 75 × 75 – 2 × 75 × 25 + 25 × 25 is 2500.
Important Questions from Identities
(x - y) 3+ (y - z) 3+ (z - x) 3= ?
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- \((\sqrt{7} + \sqrt{9})(\sqrt{7} - \sqrt{9})\) is equal to:
If x satisfies the equation x 2 - 2x + 1 = 0, then the value of \(\rm x^3 - \frac{1}{x^3}\) is:
If x + y = 5 and xy = 6, then find x 3+ y 3
