(1%E2%88%923x)-in-standard-form.jpeg "(6x+1)(1−3x) In Standard Form")
Expanding and Simplifying (6x+1)(1−3x)
This article will guide you through the process of expanding and simplifying the expression (6x+1)(1−3x) into standard form.
Understanding Standard Form
Standard form for a polynomial refers to the arrangement of terms in descending order of their exponents. For example, a quadratic expression in standard form would be ax² + bx + c.
Expanding the Expression
To expand the expression, we will use the FOIL method (First, Outer, Inner, Last).
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First: Multiply the first terms of each binomial: (6x)(1) = 6x
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Outer: Multiply the outer terms of the binomials: (6x)(-3x) = -18x²
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Inner: Multiply the inner terms of the binomials: (1)(1) = 1
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Last: Multiply the last terms of each binomial: (1)(-3x) = -3x
Now we have: 6x - 18x² + 1 - 3x
Simplifying the Expression
Combine the like terms:
- -18x² (highest exponent term)
- 6x - 3x = 3x
- 1 (constant term)
Therefore, the simplified expression in standard form is -18x² + 3x + 1.