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3 years ago

Which of the following is the correct expansion of (y + 1)(y2 + 2y + 3)?

Mathematics

1 answer:

bija089 [108]3 years ago

4 0

Use distributive property:

(a + b)(c + d) = ac + ad + bc + bd

(y + 1)(y² + 2y + 3) = (y)(y²) + (y)(2y) + (y)(3) + (1)(y²) + (1)(2y) + (1)(3)

= y³ + 2y² + 3y + y² + 2y + 3 = y³ + (2y² + y²) + (3y + 2y) + 3

= y³ + 3y² + 5y + 3

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<h3>Standard form</h3>

We can subtract the right-side expression from both sides to get standard form.

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-3x² -8 -5x +7 = 0 . . . . . . . simplify a bit

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The standard form equation can be written ...

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<h3>Coefficients</h3>

The quadratic coefficient is the coefficient of the term with degree 2. The quadratic coefficient is -3.

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Additional comment

We can make the leading coefficient positive by multiplying the equation by -1. This gives ...

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This is a legitimate answer to this question. In the case of linear equations, the "standard form" has the constant on the right side of the equal sign, and the leading coefficient is required to be positive. A negative leading coefficient can sometimes lead to errors (when the sign is overlooked), so having a positive leading coefficient is often preferred.

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