Question

N=3×5²+x express 5N² as a product of prime factors in index form give your answer in terms of x

Answer 1

Answer:

$x^{2}+(2*3*5^{2})x+3^{2}*5^{4}$

Step-by-step explanation:

Given,

$N=3*5^{2}+x$

We know,

$(a+b)^{2} = a^{2}+b^{2}+2ab$

And we know,

$(a^{m})^{n}=a^{m*n}$

So,

$5N^{2} = (3*5^{2}+x)^{2}=(3*5^{2})^2+x^{2}+2*(3*5^{2})*x\\=3^{2}*5^{4}+x^{2}+2*3*5^{2}*x\\=x^{2}+(2*3*5^{2})x+3^{2}*5^{4}$