Question

Determine which polynomial is a perfect square trinomial.

Answer 1

Answer:

16x² − 56x + 49

Step-by-step explanation:

The square of difference of two terms can be expressed as a perfect square trinomial in the following manner:

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

The symbol with square terms must be always positive. So this removes the first two options from the given choices. The correct option is either c or d.

Only the option d can be expressed as a perfect square as shown below:

$16x^{2}-56x+49\\\\ = (4x)^{2}-2(4x)(7)+(7)^{2}\\\\ =(4x - 7)^{2}$

Option c would have been correct if it was -30b instead of -15b i.e. the middle term is twice the product of first and second term.

So, option D is correct