which shows a perfect square trinomial?\n50y² - 4x²\n100 - 36x²y²\n16x² + 24xy + 9y²\n49x² - 70xy + 10y²

Answer

Explanation:

Step1: Recall perfect - square trinomial formula

The formula for a perfect - square trinomial is ((a\pm b)^2=a^{2}\pm2ab + b^{2}).

Step2: Analyze option 1

For (50y^{2}-4x^{2}), it is a difference of two terms, not a trinomial, so it is not a perfect - square trinomial.

Step3: Analyze option 2

For (100 - 36x^{2}y^{2}), it is a difference of two terms ((10^{2}-(6xy)^{2})), not a trinomial, so it is not a perfect - square trinomial.

Step4: Analyze option 3

For (16x^{2}+24xy + 9y^{2}), we have (a = 4x), (b=3y), and (2ab=2\times4x\times3y = 24xy), and (a^{2}=16x^{2}), (b^{2}=9y^{2}). So (16x^{2}+24xy + 9y^{2}=(4x + 3y)^{2}), it is a perfect - square trinomial.

Step5: Analyze option 4

For (49x^{2}-70xy + 10y^{2}), if it is in the form ((a - b)^2=a^{2}-2ab + b^{2}), when (a = 7x), (2ab=70xy) gives (b = 5y), but (b^{2}=25y^{2}\neq10y^{2}), so it is not a perfect - square trinomial.

Answer:

C. (16x^{2}+24xy + 9y^{2})