Question

select a suitable identity and find (ax2+by2)(ax2+by2)

Answer 1

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Answer 2

The using suitable identity $(ax^{2}+by^{2})(ax^{2}+by^{2})$ is $a^{2} x^{4}+b^{2} y^{4}+2abx^{2}y^{2}.$.

Step-by-step explanation:

We have,

$(ax^{2}+by^{2})(ax^{2}+by^{2})$

To find, using suitable identity $(ax^{2}+by^{2})(ax^{2}+by^{2})=?$

∴ $(ax^{2}+by^{2})(ax^{2}+by^{2})$       ....(1)

Let $p=ax^{2}$ and $q=by^{2}$

Equation (1) becomes,

$(p+q)(p+q)$

$=(p+q)^{2}$

$=p^{2}+q^{2}+2pq$

Put $p=ax^{2}$ and $q=by^{2}$, we get

$=(ax^{2})^{2}+(by^{2})^{2}+2(ax^{2})(by^{2})$

$=a^{2} x^{4}+b^{2} y^{4}+2abx^{2}y^{2}$

Hence, the using suitable identity $(ax^{2}+by^{2})(ax^{2}+by^{2})$ is $a^{2} x^{4}+b^{2} y^{4}+2abx^{2}y^{2}$.