Please factor these- 30 points

g^2 - 64h^6

k^4 - 25k^2

5r^2 + 9r - 18

Step-by-step 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)

(g - 8h³)(g + 8h³)

k²(k- 5)(k + 5)

(r + 3)(5r - 6)

Step-by-step 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)

step-by-step explanation:

this can be solved first with pythagorean theorem, which tells us to square both legs of the triangle and sum it. this will be equal to the square of the hypotenuse.

the hypotenuse is the side "opposite" the 90 degree angle, which is x.

so we can write using pythagorean theorem,

simplifying:

to further simplify this radical, we need to use the property  

thus