Question - Solving the Expression with Distribution and Expansion
mathfoil methodsolving expressionssimplify algebraic expressionsdistribution methodexpansion technique
Solution:
To solve the expression given in the image:1. Distribute the $$ 3p $$ across $$ (p - q) $$:\[ 3p \cdot p + 3p \cdot (-q) \]2. Expand the square $$ (2p - q)^2 $$ using the FOIL (First, Outer, Inner, Last) method:\[ (2p - q)(2p - q) \]\[ 2p \cdot 2p + 2p \cdot (-q) + (-q) \cdot 2p + (-q) \cdot (-q) \]Combine the above expansions:\[ 3p^2 - 3pq - (4p^2 - 2pq - 2pq + q^2) \]3. Expand the negative sign into the second parenthesis:\[ 3p^2 - 3pq - 4p^2 + 2pq + 2pq - q^2 \]4. Combine like terms:\[ 3p^2 - 4p^2 - 3pq + 2pq + 2pq - q^2 \]\[ -p^2 + pq - q^2 \]Therefore:\[ 3p(p - q) - (2p - q)^2 = -p^2 + pq - q^2 \]
CamTutor
In regards to math, we are professionals.
Get In Touch
Email: camtutor.ai@gmail.com