1. The problem is to verify or simplify the expression given as $(y-1)(3y+7)$. 2. The formula used here is the distributive property: $a(b+c) = ab + ac$. 3. Apply the distributive property to expand the expression: $$ (y-1)(3y+7) = y(3y+7) - 1(3y+7) $$ 4. Multiply each term: $$ = 3y^2 + 7y - 3y - 7 $$ 5. Combine like terms: $$ = 3y^2 + (7y - 3y) - 7 = 3y^2 + 4y - 7 $$ 6. The simplified form of the expression is $3y^2 + 4y - 7$. This shows the expanded polynomial form of the product $(y-1)(3y+7)$.