Related questions with answers

An isomorphism from the Boolean algebra with set B={0,1,a,a′}B=\left\{0,1, a, a^{\prime}\right\} to the Boolean algebra with set ℘({1,2})\wp(\{1,2\}) was defined in this section. Because the two Boolean algebras are essentially the same, an operation in one can be simulated by mapping to the other, operating there, and mapping back. a. Use the Boolean algebra on ℘({1,2})\wp(\{1,2\}) to simulate the computation 1⋅a′1 \cdot a^{\prime} in the Boolean algebra on B. b. Use the Boolean algebra on ℘({1,2})\wp(\{1,2\}) to simulate the computation (a)′(a)^{\prime} in the Boolean algebra on B. c. Use the Boolean algebra on B to simulate the computation {1}∪{2}\{1\} \cup\{2\} in the Boolean algebra on ℘({1,2}).\wp(\{1,2\}).

Question

Multiply algebraically. Use algebra tiles to help. m(15 - m)

Solution

Verified
Step 1
1 of 2

Use the Distributive Property: a(b+c)=ab+aca(b+c)=ab+ac

m(15−m)=m(15)−m(m)m(15-m)=m(15)-m(m)

Use the Law of Exponent: am⋅an=am+na^m\cdot a^n=a^{m+n}

=15m−m1+1=15m-m^{1+1}

Simplify:

=15m−m2(1)=\color{#c34632}15m-m^2\color{white}\tag{1}

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