To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.
(color(red)(4y^2) - color(red)(3))(color(blue)(4y^2) + color(blue)(7y) + color(blue)(2))(4y2−3)(4y2+7y+2) becomes:
(color(red)(4y^2) xx color(blue)(4y^2)) + (color(red)(4y^2) xx color(blue)(7y)) + (color(red)(4y^2) xx color(blue)(2)) - (color(red)(3) xx color(blue)(4y^2)) - (color(red)(3) xx color(blue)(7y)) - (color(red)(3) xx color(blue)(2))(4y2×4y2)+(4y2×7y)+(4y2×2)−(3×4y2)−(3×7y)−(3×2)
16y^4 + 28y^3 + 8y^2 - 12y^2 - 21y - 616y4+28y3+8y2−12y2−21y−6
We can now combine like terms:
16y^4 + 28y^3 + (8 - 12)y^2 - 21y - 616y4+28y3+(8−12)y2−21y−6
16y^4 + 28y^3 - 4y^2 - 21y - 616y4+28y3−4y2−21y−6
