Example

3(r+2s)=2t-4
a⋅(b-2)=3b
3(r+2s)=2t-4
a⋅(b-2)=3b

Question

$$(a+c)(c-d)+(a+b)(c+d)+2(ac+bd)$$

Answer

$$4*a*c+c^2-c*d+b*c+3*b*d$$

Solution


Use the FOIL method: \((a+b)(c+d)=ac+ad+bc+bd\).
\[ac-ad+{c}^{2}-cd+(a+b)(c+d)+2(ac+bd)\]
Use the FOIL method: \((a+b)(c+d)=ac+ad+bc+bd\).
\[ac-ad+{c}^{2}-cd+ac+ad+bc+bd+2(ac+bd)\]
Expand by distributing terms.
\[ac-ad+{c}^{2}-cd+ac+ad+bc+bd+2ac+2bd\]
Collect like terms.
\[(ac+ac+2ac)+(-ad+ad)+{c}^{2}-cd+bc+(bd+2bd)\]
Simplify.
\[4ac+{c}^{2}-cd+bc+3bd\]
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