Question

Decompose the following expressions into factors:

x^2y^2 - 121
9x^4 - 144y^4
25x^2y^6 - 81z^10
225 - 16a^12b^16
(x - 1)^2 - 25y^2
(5x + 2)^2 - y^8
0.09p^4 - 6.25q^6
9r^6m - 64s^2m + 10
(2x + 5y)^2 - 1628

Answer 1

To decompose the given expressions into factors, we can use various factoring techniques. Each expression requires a different approach, such as quadratic factoring, difference of squares, or factoring out a common factor.

Step-by-step explanation:

To decompose the given expressions into factors:

1. x^2y^2 - 121 = (xy - 11)(xy + 11)
2. 9x^4 - 144y^4 = 9(x^2 - 4y^2)(x^2 + 4y^2)
3. 25x^2y^6 - 81z^10 = (5xy^2 - 3z^2)(5xy^2 + 3z^2)
4. 225 - 16a^12b^16 = (15 - 4a^4b^8)(15 + 4a^4b^8)
5. (x - 1)^2 - 25y^2 is already factored
6. (5x + 2)^2 - y^8 is already factored
7. 0.09p^4 - 6.25q^6 = 0.25(0.3p^2 - 25q^3)(0.3p^2 + 25q^3)
8. 9r^6m - 64s^2m + 10 = (3rm - 2sm + 5)(3rm + 2sm - 2)
9. (2x + 5y)^2 - 1628 is already factored