Question

Factorise: (x⁴- 14x²y² - 51y⁴​​​​​​).

Answer 1

Let x²=a and y²=b,
Therefore;-
a²-14.a.b-51b²

Using the formula;- (x+my) (x+ny) = x² + (n+m).x.y + (nm)y²
I am using this formula since there is no coefficient for a².
Therefore, n+m = -14, and nm=-51

n = -17, m = 3
Therefore, a² - 14.a.b - 51b² = (a-17b) (a+3b)
Substituting a=x² and b=y²,
x⁴ - 14x²y² - 51y⁴ = (x²-17y²) (x²+3y²)