1. Expand (2x-1)(4x+5)
Solution:
(2x-1)(4x+5)
FOIL method : (a+b)(c+d)=ac+ad+bc+bd
=(color{red}{2x}+color{blue}{(-1)})(color{green}{4x}+color{purple}{5})
=color{red}{2x}*(color{green}{4x}+color{purple}{5})+color{blue}{(-1)}*(color{green}{4x}+color{purple}{5})
=color{red}{2x}*color{green}{4x}+color{red}{2x}*color{purple}{5}+color{blue}{(-1)}*color{green}{4x}+color{blue}{(-1)}*color{purple}{5}
=8x^2+10x+(-4x)+(-5)
=8x^2+6x-5
2. Expand (3x-1)(2x-3)
Solution:
(3x-1)(2x-3)
FOIL method : (a+b)(c+d)=ac+ad+bc+bd
=(color{red}{3x}+color{blue}{(-1)})(color{green}{2x}+color{purple}{(-3)})
=color{red}{3x}*(color{green}{2x}+color{purple}{(-3)})+color{blue}{(-1)}*(color{green}{2x}+color{purple}{(-3)})
=color{red}{3x}*color{green}{2x}+color{red}{3x}*color{purple}{(-3)}+color{blue}{(-1)}*color{green}{2x}+color{blue}{(-1)}*color{purple}{(-3)}
=6x^2+(-9x)+(-2x)+3
=6x^2-11x+3
3. Expand (7x+5)(4x+3)
Solution:
(7x+5)(4x+3)
FOIL method : (a+b)(c+d)=ac+ad+bc+bd
=(color{red}{7x}+color{blue}{5})(color{green}{4x}+color{purple}{3})
=color{red}{7x}*(color{green}{4x}+color{purple}{3})+color{blue}{5}*(color{green}{4x}+color{purple}{3})
=color{red}{7x}*color{green}{4x}+color{red}{7x}*color{purple}{3}+color{blue}{5}*color{green}{4x}+color{blue}{5}*color{purple}{3}
=28x^2+21x+20x+15
=28x^2+41x+15
4. Expand (2x-5)(x^2+3)
Solution:
(2x-5)(x^2+3)
FOIL method : (a+b)(c+d)=ac+ad+bc+bd
=(color{red}{2x}+color{blue}{(-5)})(color{green}{x^2}+color{purple}{3})
=color{red}{2x}*(color{green}{x^2}+color{purple}{3})+color{blue}{(-5)}*(color{green}{x^2}+color{purple}{3})
=color{red}{2x}*color{green}{x^2}+color{red}{2x}*color{purple}{3}+color{blue}{(-5)}*color{green}{x^2}+color{blue}{(-5)}*color{purple}{3}
=2x^3+6x+(-5x^2)+(-15)
=2x^3-5x^2+6x-15
5. Expand (2x-1)(x+5)
Solution:
(2x-1)(x+5)
FOIL method : (a+b)(c+d)=ac+ad+bc+bd
=(color{red}{2x}+color{blue}{(-1)})(color{green}{x}+color{purple}{5})
=color{red}{2x}*(color{green}{x}+color{purple}{5})+color{blue}{(-1)}*(color{green}{x}+color{purple}{5})
=color{red}{2x}*color{green}{x}+color{red}{2x}*color{purple}{5}+color{blue}{(-1)}*color{green}{x}+color{blue}{(-1)}*color{purple}{5}
=2x^2+10x+(-x)+(-5)
=2x^2+9x-5
This material is intended as a summary. Use your textbook for detail explanation.
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