Question

Select the perfect square trinomial for each polynomial. (There are 2 correct answers)

Answer 1

Answer:

x^2−18x+81

x^2+2x+1

Step-by-step explanation:

we know that

A trinomial is a perfect square trinomial if it can be factored into a binomial multiplied to itself

so

$a^2\pm2ab+b^2=(a\pm b)(a\pm b)=(a\pm b)^2$

Verify each case

case a) x^2−10x−25

we know that

$(x-5)^2=x^2-10x+25$

therefore

Is not a perfect square trinomial

case b) x^2−18x+81

we know that

$(x-9)^2=x^2-18x+81$

therefore

Is a perfect square trinomial

case c) x^2+2x+1

we know that

$(x+1)^2=x^2+2x+1$

therefore

Is a perfect square trinomial

case d) x^2+7x+49

we know that

$(x+3.5)^2=x^2+7x+12.25$

therefore

Is not a perfect square trinomial