Question

Select the polynomial that is a perfect square trinomial.

a) 49x2 − 8x + 16
b)4a2 − 10a + 25
c) 25b2 − 5b + 10
d) 16x2 − 8x + 1

Answer 1

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


$a)\ 49x^2-8x+16=(7x)^2-2\cdot x\cdot4+4^2-NOT\\\\b)\ 4a^2-10a+25=(2a)^2-2\cdot a\cdot5+5^2-NOT\\\\c)\ 25b^2-5b+10=(5b)^2-5b+10-NOT\\\\d)\ 16x^2-8x+1=(4x)^2-2\cdot4x\cdot1+1^2=(4x-1)^2-YES!$

$\text{Answer: d)}$