Removing brackets from an expression is known as expanding the expression. This usually occurs when a term outside a bracket is multiplied by each of the terms inside the bracket.
Distributive Property
Multiplication is said to be distributive over addition and subtraction. The outside term "distributes" itself over the inside terms.
e.g. 3(x + 4) = 3.x + 3.4 = 3x + 12
4(p − 5) = 4.p − 4.5 = 4p − 20
Examples |
Answers |
Expand and simplify:
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2(x + 7)
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= 2x + 14
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5(3x − 6)
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= 15x − 30
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-2(4 − 3x)
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= -8 + 6x
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4a(a − 3)
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= 4a2 − 12a
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3(x + 7) + 4(x − 2)
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= 3x + 21 + 4x − 8
= 7x + 13
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4x − 3(2x + 3 + 4y)
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= 4x − 6x − 9 − 12y
= -2x − 12y − 9
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CARE! The most common mistake with expanding brackets is when there is a negative term outside the bracket.
e.g. 3 − 2(x − 4) = 3 − 2x + 8 = 11 − 2x.
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