Question

2)52²-25²/79²-51² 3)181²-61²/319²-77²4)200²-380²/420²-160²​

Answer 1

2) (52²-25²)/(79²-51²) = (52-25)(52+25) / (79-51)(79+51) = (27*77) / (28*130) = (27*11) / (4*130) = 297/520

3)(181²-61²)/(319²-77²) = (181-61)(181+61) / (319-77)(319+77) = (120*242) / (242*396) = 30/99 = 10/33

4)(200²-380²)/(420²-160²​) = (200-380)(200+380) / (420-160)(420+160) = (-180*580)/(260*580) = -9/13

Answer 2

To simplify the expressions, I'll perform the calculations step by step:

1. $\frac{{52^2 - 25^2}}{{79^2 - 51^2}}$

Step 1: Calculate the numerators and denominators.

Numerator: $52^2 - 25^2 = 2704 - 625 = 2079$

Denominator: $79^2 - 51^2 = 6241 - 2601 = 3640$

Step 2: Divide the numerator by the denominator.

Result: $\frac{{2079}}{{3640}}$

2. $\frac{{181^2 - 61^2}}{{319^2 - 77^2}}$

Step 1: Calculate the numerators and denominators.

Numerator: $181^2 - 61^2 = 32761 - 3721 = 29040$

Denominator: $319^2 - 77^2 = 101761 - 5929 = 95632$

Step 2: Divide the numerator by the denominator.

Result: $\frac{{29040}}{{95632}}$

3. $\frac{{200^2 - 380^2}}{{420^2 - 160^2}}$

Step 1: Calculate the numerators and denominators.

Numerator: $200^2 - 380^2 = 40000 - 144400 = -104400$

Denominator: $420^2 - 160^2 = 176400 - 25600 = 150800$

Step 2: Divide the numerator by the denominator.

Result: $\frac{{-104400}}{{150800}}$

Please note that these results are in fractional form and can be further simplified if needed. Also, if you have any other mathematical questions or need further assistance, feel free to ask!