# Distributive Property is used to expand an expression Why: it makes it easier to solve.

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Distributive Property is used to expand an expression Why: it makes it easier to solve

Recall the distributive property of multiplication over addition... symbolically: a × (b + c) = a × b + a × c and pictorially (rectangular array area model): a × ba × ca bc

An example: 6 x 13 using your mental math skills... symbolically: 6 × (10 + 3) = 6 × 10 + 6 × 3 and pictorially (rectangular array area model): 6 × 106 × 36 103

What about 12 x 23? Mental math skills? (10+2)(20+3) = 10 × 20 + 10 × 3 + 2 × 20 + 2 × 3 10 × 20 10 × 3 10 203 2 × 32 × 322 × 20 200 30 40 + 6 276

Distributive Property (a+b) × (c+d) = a × (c+d) + b × (c+d) = a × c + a × d + b × c + b × d a × c a × d a c d b × db × dbb × c

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