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Polynomial Arithmetic

Applying the Perfect Square Identity


If x2+20xy+100y2=(x+ay)2,x^2+20xy+100y^2=(x+ay)^2, what is the value of aa?

If x2+121(xa)2=22x,x^2+121-(x-a)^2=22x, what is the value of aa?

If 16x2+56xy+49y2=(ax+by)2,16x^2+56xy+49y^2=(ax+by)^2, what is the value of abab?

Given ab=42+126,bc=42126,a-b=\sqrt{42+12\sqrt{6}}, b-c=\sqrt{42-12\sqrt{6}}, what is the value of a2+b2+c2abbcca?a^2+b^2+c^2-ab-bc-ca?

What is the coefficient of xx in the expansion of (x+3)2 (x+3 ) ^ 2 ?


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