Question

Factorise 21x^2-14y^2

Answer 1

`\large\boxed{21x^4-14y^2=7(3x^4-2y^2)=7(x^2\sqrt3-y\sqrt2)(x^2\sqrt3+y\sqrt2)}`

Explanation:

`21x^4-14y^2=7(3x^4-2y^2)\\\\=7\bigg((\sqrt3)^2x^(2\cdot2)-(\sqrt2)^2y^2\bigg)\qquad\text{use}\ (a^n)^m=a^(nm)\ \text{and}\ (ab)^n=a^nb^n\\\\=7\bigg((x^2\sqrt3)^2-(y\sqrt2)^2\bigg)\qquad\text{use}\ a^2-b^2=(a-b)(a+b)\\\\=7(x^2\sqrt3-y\sqrt2)(x^2\sqrt3+y\sqrt2)`