Answer:
[tex]AB + A = 16[/tex]
Step-by-step explanation:
Given
[tex]12y^2 - 65y + 42 = (Ay -14)(By - 3)[/tex]
Required
Find [tex]AB + A[/tex]
[tex]12y^2 - 65y + 42 = (Ay -14)(By - 3)[/tex]
Expand
[tex]12y^2 -56y -9y + 42 = (Ay - 14)(By -3)[/tex]
Factorize
[tex]4y(3y -14) -3(3y - 14) = (Ay - 14)(By -3)[/tex]
Factor out 3y- 14
[tex](3y - 14)(4y -3) = (Ay - 14)(By -3)[/tex]
By comparison:
[tex]Ay - 14 = 3y - 14[/tex]
and
[tex]By - 3 = 4y - 3[/tex]
So, we have:
[tex]Ay - 14 = 3y - 14[/tex]
Add 14 to both sides
[tex]Ay = 3y[/tex]
Divide both sides by y
[tex]A = 3[/tex]
[tex]By - 3 = 4y - 3[/tex]
Add 3 to both sides
[tex]By = 4y[/tex]
Divide both sides by y
[tex]B = 4[/tex]
So, the expression [tex]AB + A[/tex] is:
[tex]AB + A = 3 * 4 + 4[/tex]
[tex]AB + A = 12 + 4[/tex]
[tex]AB + A = 16[/tex]
