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2 years ago

What is the product of a+3 and −2a2+15a+6b2?

Mathematics

2 answers:

zhannawk [14.2K]2 years ago

8 0

Answer:

-2a³+9a²+45a+6ab²+18b²

Step-by-step explanation:

(a+3)(-2a²+15a+6b²)

Distribute the a:

-2a³+15a²+6ab²

Then distribute the 3:

-6a²+45a+18b²

Now add both of the results together:

-2a³+15a²+6ab²-6a²+45a+18b²

Combine like terms:

-2a³+9a²+45a+6ab²+18b²

o-na [289]2 years ago

6 0

Answer:

Step-by-step explanation:

Examination of the answer choices shows us we only need to be concerned with the a^2 term and the b^2 term.

The a^2 term will be the sum of products ...

3(-2a^2) +a(15a) = (-6 +15)a^2 = +9a^2

The b^2 term will be the product ...

3(6b^2) = 18b^2

These terms are sufficient to identify choice C as the correct answer choice.

_____

<em>Additional comment</em>

It can often work well to develop the product of polynomials by considering the terms that must contribute to a given product term. For a term containing a^2, the product of polynomial terms can have that degree if and only if it is the product of a constant and an a^2 term, or the product of two a^1 terms. The ways those products can be achieved are shown in the above working.

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Which is the correct way to solve the given equation

Karolina [17]

Option 2. $x = \frac{4 \pm \sqrt{(-4)^{2}-4 (1)(-21)}}{2 (1)}$ shows the correct way to use the quadratic formula to solve the given equation.

Step-by-step explanation:

Step 1:

For an equation of the form $ax^{2} +bx+c=0$ the solution is $x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$ .

Here a is the coefficient of $x^{2}$ , b is the coefficient of x and c is the constant term.

$x^{2} -4x=21$ can also be written as $x^{2} -4x-21=0.$

Comparing $x^{2} -4x-21=0$ with $ax^{2} +bx+c=0$ , we get that a is 1, b is -4 and c is -21.

To get the solution, we substitute the values of a, b, and c in $x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$ .

Step 2:

Substituting the values, we get

$x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}= \frac{-(-4) \pm \sqrt{(-4)^{2}-4 (1)(-21)}}{2 (1)}.$

$\frac{-(-4) \pm \sqrt{(-4)^{2}-4 (1)(-21)}}{2 (1)} = \frac{4 \pm \sqrt{(-4)^{2}-4 (1)(-21)}}{2 (1)}.$

This is option 2.

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seraphim [82]

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=3*15*20
=900 square units.

However, a hexagon consists of 6 equilateral triangles in which the apothem is 0.866 times the base, meaning that the apothem is shorter than the base.
Perhaps the base is 20 and apothem 15. The answer will come to be the same though.

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2 years ago

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Is D
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