Factor 9y2 - 12y + 4. (3 y - 2)(3 y + 2) (3 y - 4)( y + 1) (3 y - 2) 2

Mathematics

1 answer:

lozanna [386]3 years ago

8 0

Answer:

(y - 2)²

Step-by-step explanation:

9y² - 12y + 4 ← is a perfect square of the form

(ax - b)² = a²x² - 2abx + b²

Compare like terms with 9y² - 12y + 4, thus

a² = 9 ⇒ a = 3

b² = 4 ⇒ b = 2 and

- 2ab = - 2 × 3 × 2 = - 12

Thus

9y² - 12y + 4 = (3y - 2)²

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Simplify.<br> Rewrite the expression in the form b^n<br><br> (b^3)^2

Alexxandr [17]

Step-by-step explanation:

$a^n={\underbrace{a\cdot a\cdot a\cdot...\cdot a}_{n}$

<h2>METHOD 1.</h2>

$\left(b^3\right)^2=\underbrace{b^3\cdot b^3}_{2}=\underbrace{b\cdot b\cdot b}_{3}\cdot\underbrace{b\cdot b\cdot b}_{3}=\underbrace{b\cdot b\cdot b\cdot b\cdot b\cdot b}_{6}=b^6$

<h2>METHOD 2.</h2>

$\left(b^3\right)^2=\underbrace{b^3\cdot b^3}_{2}=b^{3+3}=b^6\qquad\text{used}\ a^n\cdot a^m=a^{n+m}$

<h2>METHOD 3.</h2>

$\left(b^3\right)^2=\left(\underbrace{b\cdot b\cdot b}_{3}\right)^2=b^2\cdot b^2\cdot b^2=b^{2+2+2}=b^6\\\text{used}\ (ab)^n=a^nb^n,\ a^n\cdot a^m=a^{n+m}$