Aling expression ang ganap na factored form ng x ^ 6-64y ^ 3?

Sagot:

# x ^ 6-64y ^ 3 = (x ^ 2-4y) (x ^ 2 + 2xsqrt (y) + 4y) (x ^ 2-2xsqrt (y) + 4y) #

Paliwanag:

# x ^ 6-64y ^ 3 #

# = (x ^ 2) ^ 3 (4y) ^ 3 #

# = (x ^ 2-4y)) (x ^ 4 + 4x ^ 2y + 16y ^ 2) #

# = (x ^ 2-4y) (x ^ 2) ^ 2 + (4y) ^ 2 + 4x ^ 2y) #

# = (x ^ 2-4y) (x ^ 2 + 4y) ^ 2-2 * x ^ 2 * 4y + 4x ^ 2y) #

# = (x ^ 2-4y) (x ^ 2 + 4y) ^ 2-8x ^ 2y + 4x ^ 2y) #

# = (x ^ 2-4y) (x ^ 2 + 4y) ^ 2- (2xsqrt (y)) ^ 2 #

# = (x ^ 2-4y) (x ^ 2 + 2xsqrt (y) + 4y) (x ^ 2-2xsqrt (y) + 4y) #

Sagot:

# (x ^ 2 - 4y) (x ^ 4 + x ^ (2) 4y + 16y ^ 2) #

Paliwanag:

# x ^ 6-64y ^ 3 #

Kung isulat namin ito bilang:

# (x ^ 2) ^ 3- (4y) ^ 3 #: Ito ang pagkakaiba ng dalawang cubes:

# (a ^ 3-b ^ 3) = (a-b) (a ^ 2 + ab + b ^ 2) #

Kaya:

# ((x ^ 2) ^ 3 (4y) ^ 3) = (x ^ 2 - 4y) (x ^ 4 + x ^ (2) 4y + 16y ^ 2) #