Question

Which trinomials are perfect square trinomials?

Answer 1

ANSWER

B. ${m}^{2}+10m+25$

D. ${m}^{2} + 24m+144$

EXPLANATION

A perfect square trinomial is of the form;

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

or

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

For option A,

${m}^{2} + 2(5)m + {10}^{2} \ne \: {(m + 10)}^{2}$

This is not a perfect square trinomial.

For option B

${m}^{2} + 2(5)m + {5}^{2} = \: {(m + 5)}^{2}$

This is a perfect square trinomial.

For option C

${m}^{2} + 2(18)m + {6}^{2} \ne \: {(m + 6)}^{2} .$

This is not a perfect square trinomial.

For option D.

${m}^{2} + 2(12)m + {12}^{2} = \: {(m + 12)}^{2}$

This is a perfect square trinomial.

The correct answers are option B and D.

Answer 2

Perfect square is
a²+2ab+b²

so just take the square root of the end ones and add then double to get middle term


A.
m+10=10m, doubled is 20m
nope

B.
m+5=5m, doubled is 10m, yep

C.
m+2√15=fancy thing that won't get to 36m

D.
m+12=12m, doubled is 24m, yep


B and D