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Expanding the Expression (x+5)(x+6)(x+7)
This article will guide you through the process of expanding the expression (x+5)(x+6)(x+7). We will use the distributive property to multiply the binomials step by step.
Step 1: Multiply the First Two Binomials
Begin by multiplying the first two binomials: (x+5)(x+6).
(x+5)(x+6) = x(x+6) + 5(x+6)
Applying the distributive property again:
= x² + 6x + 5x + 30
Combining like terms:
= x² + 11x + 30
Step 2: Multiply the Result by the Third Binomial
Now, we multiply the result from step 1 (x² + 11x + 30) by the third binomial (x+7).
(x² + 11x + 30)(x+7) = x²(x+7) + 11x(x+7) + 30(x+7)
Applying the distributive property:
= x³ + 7x² + 11x² + 77x + 30x + 210
Combining like terms:
= x³ + 18x² + 107x + 210
Conclusion
Therefore, the expanded form of the expression (x+5)(x+6)(x+7) is x³ + 18x² + 107x + 210.