Expand (x − 2)³
Worked out line by line the way a teacher would write it.
Answer
| Expanded form | x³ − 6x² + 12x − 8 |
Step-by-step solution
6 steps-
1 Given\left(x - 2\right)^{3}
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2 Write the power as a repeated product
A power is repeated multiplication: (a + b)² = (a + b)(a + b). Writing it out shows exactly which brackets to multiply.
\left(x - 2\right) \left(x - 2\right) \left(x - 2\right) -
3 Multiply the binomials (FOIL: First, Outer, Inner, Last)
To multiply two binomials, multiply every term of one by every term of the other: the First terms, the Outer terms, the Inner terms and the Last terms, four products in all.
\left(x \cdot x + x \cdot (-2) + (-2) \cdot x + (-2) \cdot (-2)\right) x - 2 -
4 Multiply out and combine like terms\left(x - 2\right) \left(x^{2} - 4 x + 4\right)
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5 Distribute: multiply every term of the first bracket by every term of the second
Every term of the first bracket multiplies every term of the second, then like terms are combined.
\left(x \cdot x^{2} + x \cdot (- 4 x) + x \cdot 4 + (-2) \cdot x^{2} + (-2) \cdot (- 4 x) + (-2) \cdot 4\right) -
6 Multiply out and combine like termsx^{3} - 6 x^{2} + 12 x - 8
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