Factor 100x^2-20xy+y^2 enter your answer in the box

Accepted Solution

Answer:[tex](10x-y)^{2}[/tex]Step-by-step explanation:In order to factor the given trinomial, you can rewrite it as follows:The square root of the first term [tex]100x^{2}[/tex] is:[tex]\sqrt{100x^{2} } = \sqrt{100}(\sqrt{x^{2} }) = 10x[/tex]The square root of the last term [tex]y^{2}[/tex] is:[tex]\sqrt{y^{2} } = y[/tex]So you can rewrite it as:[tex](10x)^{2} -20xy + (y)^{2}[/tex]The term -20xy can be written as: -2(10xy)So, notice that the first and last term are perfect squares and the other term is two times the product of the first and last terms. Because of that, you can use the Perfect Square Trinomials form which is:[tex](ax)^{2} - 2axb + (b)^{2} = (ax-b)^{2}[/tex]In this case, a=10 and b=yThen you obtain:[tex](10x-y)^{2}[/tex]