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Enter the mathematical expression to simplify it by applying the distributive law, with step-by-step details.
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This distributive property calculator helps you quickly simplify expressions by applying the distributive property of multiplication over addition or subtraction.
The distributive property in mathematics states that multiplying a number by a sum or difference inside parentheses is the same as multiplying the number by each term separately and then combining the results. It is a fundamental tool for simplifying expressions efficiently.
General form:
a × (b + c) = a × b + a × c
Here are some examples to demonstrate its use.
Simplify: 19 × (67 + 3)
Solution:
Apply the distributive property: (a + b) × c = a × c + b × c
So:
19 × (67 + 3) = 19 × 67 + 19 × 3 = 1273 + 57 = 1330
Simplify: (7 - 5) × 9
Solution:
Subtracting is equivalent to adding a negative:
(7 - 5) × 9 = 7 × 9 - 5 × 9 = 63 - 45 = 18
Simplify: (3 + 9 - 12) × (22 - 0.2 + 2)
Solution:
Step 1: Multiply each term individually:
(3 × 22) + (3 × -0.2) + (3 × 2) + (9 × 22) + (9 × -0.2) + (9 × 2) + (-12 × 22) + (-12 × -0.2) + (-12 × 2)
Step 2: Perform the multiplications:
66 - 0.6 + 6 + 198 - 1.8 + 18 - 264 + 2.4 - 24
Step 3: Combine like terms:
(66 + 6 + 198 + 18 - 264 - 24) + (-0.6 - 1.8 + 2.4) = 0 + 0 = 0
Result: 0
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