Question

Please factor these- 30 points

g^2 - 64h^6

k^4 - 25k^2

5r^2 + 9r - 18

Answer 1

(g - 8h³)(g + 8h³)

k²(k- 5)(k + 5)

(r + 3)(5r - 6)

Explanation:

g^2 - 64h^6

g² - (8h³)²

(g - 8h³)(g + 8h³)

k^4 - 25k^2

k²(k² - 25)

k²(k² - 5²)

k²(k- 5)(k + 5)

5r^2 + 9r - 18

5r² + 15r - 6r - 18

5r(r + 3) - 6(r + 3)

(r + 3)(5r - 6)

Answer 2

Explanation:

For the first one, factor using difference of squares.

g² − 64h⁶ = (g − 8h³) (g + 8h³)

For the second one, factor out the greatest common factor, then factor the difference of squares.

k⁴ − 25k² = k² (k² − 25) = k² (k − 5) (k + 5)

For the third one, factor using AC method.

5×-18 = -90.

Factors of -90 that add up to +9 are -6 and +15.

Divide by 5 and reduce: -6/5, 15/5 = 3/1.

5r² + 9r − 18 = (5r − 6) (r + 3)