which diagram represents the factors of m² - 10m + 16?

Explanation:

Step1: Factor the quadratic expression

We need to factor (m^{2}-10m + 16). We look for two numbers that multiply to (16) and add up to (- 10). The numbers are (-2) and (-8) since ((-2)\times(-8)=16) and (-2+( - 8)=-10). So (m^{2}-10m + 16=(m - 2)(m - 8)).

Step2: Expand using the area - model (box - method)

When we expand ((m - 2)(m - 8)) using the box - method, the first term of the first binomial (m) is multiplied by the first term (m) and the second term (-8) of the second binomial, and the second term (-2) of the first binomial is multiplied by the first term (m) and the second term (-8) of the second binomial. The box will have (m\times m=m^{2}), (m\times(-8)=-8m), (-2\times m=-2m) and ((-2)\times(-8) = 16). The correct box should have (m) and (-8) in one row and (m) and (-2) in one column.

Answer:

The second diagram (the one with (m) and (-8) in the top - row and (m) and (2) in the left - column, since ((m - 2)(m - 8)=m^{2}-8m-2m + 16=m^{2}-10m + 16))