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2 years ago

(3x +4y)2 is equal to

Mathematics

2 answers:

SCORPION-xisa [38]2 years ago

5 0

Answer:

9x² + 24xy + 16y²

Step-by-step explanation:

(3x + 4y)²

= (3x + 4y)(3x + 4y)

each term in the second factor is multiplied by each term in the first factor.

3x(3x + 4y) + 4y(3x + 4y) ← distribute both parenthesis

= 9x² + 12xy + 12xy + 16y² ← collect like terms

= 9x² + 24xy + 16y²

Nikolay [14]2 years ago

4 0

Answer: 6x + 8y

Hope this helps!

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3 years ago

Explain how to find each root, with its multiplicity, for the polynomial y=x^5-27x^2.

Nuetrik [128]

The roots of $y = x^{5}-27\cdot x^{2}$ are 0 (multiplicity 2), -3 (multiplicity 1), $-\frac{3}{2}+i\,\frac{3\sqrt{3}}{2}$ (multiplicity 1) and $-\frac{3}{2}-i\,\frac{3\sqrt{3}}{2}$ (multiplicity 1).

The characteristics of the polynomial can be derived from algebraic techniques. Roots and multiplicity can be found by <em>factoring</em> the polynomial. The multiplicity is represented by a power binomial of the form:

$(x-r_{i})^{m},\,m \le n$ (1)

Where $n$ is the grade of the polynomial.

Now we proceed to factor the formula:

$y = x^{5}-27\cdot x^{2}$

$y = x^{2}\cdot (x^{3}-27)$

$y = x^{2}\cdot (x^{2}+3\cdot x +9)\cdot (x-3)$

Please notice that $x^{2}+3\cdot x + 9$ have two complex roots.

$y = x^{2}\cdot \left(x+\frac{3}{2}-i\,\frac{3\sqrt{3}}{2} \right)\cdot \left(x+\frac{3}{2}+i\,\frac{3\sqrt{3}}{3} \right)\cdot (x-3)$

The roots of $y = x^{5}-27\cdot x^{2}$ are 0 (multiplicity 2), -3 (multiplicity 1), $-\frac{3}{2}+i\,\frac{3\sqrt{3}}{2}$ (multiplicity 1) and $-\frac{3}{2}-i\,\frac{3\sqrt{3}}{2}$ (multiplicity 1).

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3 years ago

The lengths of the sides of a triangle are 18 km, 23 km, and 30 km. Is the triangle a right triangle, an acute triangle, or an o

babunello [35]

a^2 + b^2 = c^2 is right a^2 + b^2 > c^2 is acute a^2 + b^2 < c^2 is obtuse

a^2 + b^2 = c^2

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obtuse

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3 years ago