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
If \(2x + { {1} \over 3x}= 5, x ≠ 0\) , then what is the value of \(27x^3+{{1} \over 8x^3}\) ?
If x 2 + 4y 2 = 40, xy = 6 and x > 2y then the value of x - 2y is:
- \(\dfrac{(0.73)^3+(0.31)^3}{(0.73)^2-0.73\times0.31+(0.31)^2}\)
- \(\dfrac{(5.17-2.19)^2-(5.17+2.19)^2}{11.3223}\)
If a(a + b + c) 2= 1792; b(a + b + c) 2= 1536; c(a + b + c) 2= 768 then what will be the value of a?
