# Khan/khan-exercises

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86 lines (70 sloc) 4.242 kB
 Multiplying expressions 0.5
random() < 0.25 1 randRangeNonZero( -10, 10 ) 1 SQUARE ? B : randRangeNonZero( -10, 10 ) "x" "x^2" "\\left(" + plus( A+X, B ) + "\\right)" "\\left(" + plus( C+X, D ) + "\\right)"

LEFT + (SQUARE ? "^2" : RIGHT) = \ ?

plus((A * C) + XX, (A * D + B * C) + X, B * D)

• plus(XX, B * D)
• plus(XX, B * D)
• plus((A + C) + XX, (A * D + B * C) + X, B * D)
• plus((A * C) + XX, (A * D + B * C) + X, B + D)
• plus((A + C) + XX, (A * D + B * C) + X, B + D)
• plus((A + C) + XX, (A * D - B * C) + X, B * D)
• plus((A * C) + XX, (A * D - B * C) + X, B + D)
• plus((A + C) + XX, (A * D - B * C) + X, B + D)
• plus((A + C) + XX, (A * B + C * D) + X, B * D)
• plus((A * C) + XX, (A * B + C * D) + X, B + D)
• plus((A + C) + XX, (A * B + C * D) + X, B + D)
• plus((A + C) + XX, (A * B - C * D) + X, B * D)
• plus((A * C) + XX, (A * B - C * D) + X, B + D)
• plus((A + C) + XX, (A * B - C * D) + X, B + D)

= LEFT + RIGHT

Start by distributing the (\blue{X + B}):

Next, distribute the \blue{X} and the \blue{B}:

\qquad = \quad (\blue{X} \cdot X) + (\blue{X} \cdot D) + (\blue{B} \cdot X) + (\blue{B} \cdot D)

Notice that by distributing you're really just multiplying each term in the first expression by each term in the second expression.

Simplify:

\qquad = \quad XX + DX + BX + B * D

Keep simplifying to get the final answer:

\qquad = \quad plus(XX, (D + B) + X, (B * D))

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