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
The coefficient of y in the expansion of (2y – 5) 3, is:
If x + y = 2 and \(\frac{1}{x}+\frac{1}{y}=\frac{18}{5}\) , then the value of (x 3+ y 3) is:
If x - y = 11 and \(\rm \frac{1}{x} - \frac{1}{y} = \frac{11}{24}\) then the value of x 3 - y 3 + x 2y 2 ?
If 2x 2- 8x - 1 = 0, then what is the value of \(\rm 8x^3 - \frac{1}{x^3}\) ?
If \(\rm x+ \frac{1}{x} = 4,\) then the value of \(\rm x^5 + \frac{1}{x^5}\) is:
