All categories

2 years ago

F(x) = (3x + 6) (x - 3)²

Mathematics

1 answer:

Sever21 [200]2 years ago

5 0

f(x)= 3x³ - 18x +9

Algebraic identities are algebraic equations that are true regardless of the value of each variable. Additionally, they are employed in the factorization of polynomials. Algebraic identities are employed in this manner for the computation of algebraic expressions and the solution of various polynomials.

Identity I: (a + b)² = a² + 2ab + b²

Identity II: (a – b)² = a² – 2ab + b²

Identity III: a² – b²= (a + b)(a – b)

Identity IV: (x + a)(x + b) = x² + (a + b) x + ab

Identity V: (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca

Identity VI: (a + b)³ = a³ + b³ + 3ab (a + b)

Identity VII: (a – b)³ = a³ – b³ – 3ab (a – b)

Identity VIII: a³ + b³ + c³ – 3abc = (a + b + c)(a² + b² + c² – ab – bc – ca)

f(x) = (3x + 6) (x - 3)²

= ( 3x + 6) ( x - 3 )²

= ( 3x + 6)( x² - 6x + 9)

= 3x( x² - 6x + 9) + 6( x² - 6x + 9)

= 3x³ - 6x² + 18x + 6x² - 36x +9

= 3x³ - 18x +9

To learn more about algebraic expansions, refer to brainly.com/question/4344214

#SPJ9

You might be interested in

How much longer is a 12cm pencil than a 1 dm pen

Alexxx [7]

Well one dm= 10 cm
12-10= 2 cm

6 0

3 years ago

Directions : Factor each of the following Differences of two squares and write your answer together with solution

N76 [4]

$\huge \boxed{\mathfrak{Question} \downarrow}$

Factor each of the following differences of two squares and write your answer together with solution.

$\large \boxed{\mathbb{ANSWER\: WITH\: EXPLANATION} \downarrow}$

$\sf \: x ^ { 2 } - 36$

Rewrite $\sf\:x^{2}-36 as x^{2}-6^{2}$ . The difference of squares can be factored using the rule: $\sf\: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right)$ .

$\boxed{ \boxed{ \bf\left(x-6\right)\left(x+6\right) }}$

__________________

$\sf \: 49 - x ^ { 2 }$

Rewrite 49-x² as 7²-x². The difference of squares can be factored using the rule: $\sf\:a^{2}-b^{2}=\left(a-b\right)\left(a+b\right)$ .

$\sf \: \left(7-x\right)\left(7+x\right)$

Reorder the terms.

$\boxed{ \boxed{ \bf\left(-x+7\right)\left(x+7\right) }}$

__________________

$\sf \: 81 - c ^ { 2 }$

Rewrite 81-c²as 9²-c². The difference of squares can be factored using the rule: $\sf\:a^{2}-b^{2}=\left(a-b\right)\left(a+b\right)$ .

$\sf\left(9-c\right)\left(9+c\right)$

Reorder the terms.

$\boxed{ \boxed{ \bf\left(-c+9\right)\left(c+9\right) }}$

__________________

$\sf \: m ^ { 2 } n ^ { 2 } - 1$

Rewrite m²n² - 1 as $\sf\left(mn\right)^{2}-1^{2}$ . The difference of squares can be factored using the rule: $\sf\:a^{2}-b^{2}=\left(a-b\right)\left(a+b\right)$ .