Question

1) (а - у)(a +y)(a² +y²); 3) (х – 6у³)² : (х + 6у³)²; 5) (25х²+y²)(5х +y)(5х - у); ​

Answer 1

2. $a ^{4} - y ^{4}$
3. $\frac{x ^{2} - 12xy ^{3} 36y ^{6} }{(x +6y ^{3})^{2} }$
4. $625 {x}^{4} - {y}^{4}$

Answer 2

I see you have three expressions here, and it looks like you want to either simplify them or perform some operations on them. Let's go through each one:

1. (a - y)(a + y)(a² + y²):

You can use the difference of squares formula to simplify this expression because (a - y)(a + y) is a difference of squares. The formula is (x - y)(x + y) = x² - y².

So for this expression, you can apply the difference of squares formula:

(a - y)(a + y) = a² - y²

Now, you have a simplified expression: a² - y². However, you still have one more factor, which is (a² + y²). So the final simplified expression is:

a² - y² + (a² + y²) = 2a²

So the simplified expression is 2a².

3. (x - 6y³)² : (x + 6y³)²:

To simplify this expression, you can use the formula for the square of a difference and the square of a sum:

(x - 6y³)² = x² - 12xy³ + 36y^6 (x + 6y³)² = x² + 12xy³ + 36y^6

Now, you can divide the two expressions:

(x - 6y³)² : (x + 6y³)² = (x² - 12xy³ + 36y^6) / (x² + 12xy³ + 36y^6)

This expression cannot be simplified further.

5. (25x² + y²)(5x + y)(5x - y):

To simplify this expression, you can use the difference of squares again for the first factor:

25x² + y² = (5x)² + y² = (5x + y)(5x - y)

Now, you have:

(5x + y)(5x - y)(5x + y)(5x - y)

You can use the difference of squares again for the remaining factors:

(5x + y)(5x - y)(5x + y)(5x - y) = [(5x + y)(5x - y)]²

So, the simplified expression is:

[(5x + y)(5x - y)]²