Find the HCF from x^3 - 8y^3 and x^2 + 4x^(2)y^(2) + 16y^4
can someone pls help me to find the hcf
can someone pls help me to find the hcf
1st expression: x^3 - 8y^3
= x3 - (2y)3
= (x - 2y)(x2 + 2xy + 4y2)
2nd expression: x2 + 4x2y2 + 16y4
= x2 + (4y2)2 + 4x2y2
= (x + 4y2)2 - 8x2y2 + 4x2y2
= (x + 4y2)2 - (2xy)2
= (x + 4y2 + 2xy)(x + 4y2 - 2xy)
= (x + 2xy + 4y2)(x - 2xy + 4y2)
From above, we can find that the highest common factor (HCF) is (x + 2xy + 4y2)
Video explanation