which diagram represents the factors of $m^{2}-10m + 16$?
which diagram represents the factors of $m^{2}-10m + 16$?
Answer
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 (-8) and (-2) since ((-8)\times(-2)=16) and (-8+( - 2)=-10). So (m^{2}-10m + 16=(m - 8)(m - 2)).
Step2: Expand the factored form using a table
When we expand ((m - 8)(m - 2)) using a table, the first - row elements are (m) and (-8), and the first - column elements are (m) and (-2). The product of the first - row and first - column elements gives the terms of the expansion. (m\times m=m^{2}), (m\times(-8)=-8m), (-2\times m=-2m), (-2\times(-8) = 16).
Answer:
The second diagram (where the first - row elements are (m) and (-8) and the first - column elements are (m) and (2)) represents the factors of (m^{2}-10m + 16) because ((m - 8)(m - 2)=m^{2}-8m-2m + 16=m^{2}-10m + 16).