Respuesta :
Answer:
1.
Option B and D are correct.
2.
Option C and D are correct.
Step-by-step explanation:
1.
A.
Take RHS
[tex]2x^3(4-3x^3)[/tex]
Using distributive property: [tex]a\cdot (b+c) = a\cdot b+ a\cdot c[/tex]
[tex]8x^3-6x^6[/tex] ∵[tex]x^a \cdot x^b = x^{a+b}[/tex]
then;
[tex]8x^3-6x \neq 2x^3(4-3x^3)[/tex]
Similarly;
B.
[tex]6x^3(5x-2)[/tex]
Using distributive property: [tex]a\cdot (b+c) = a\cdot b+ a\cdot c[/tex]
[tex]30x^4-12x^3[/tex] ∵[tex]x^a \cdot x^b = x^{a+b}[/tex]
then;
[tex]30x^4-12x^3 = 6x^3(5x-2)[/tex]
C.
[tex]5x^3(20x+1)[/tex]
Using distributive property: [tex]a\cdot (b+c) = a\cdot b+ a\cdot c[/tex]
[tex]100x^4+5x^3[/tex] ∵[tex]x^a \cdot x^b = x^{a+b}[/tex]
then;
[tex]100x^3+5 \neq 5x^3(20x+1)[/tex]
D.
[tex]2x(2x+5)[/tex]
Using distributive property: [tex]a\cdot (b+c) = a\cdot b+ a\cdot c[/tex]
[tex]4x^2+10x[/tex] ∵[tex]x^a \cdot x^b = x^{a+b}[/tex]
then;
[tex]4x^2+10x = 2x(2x+5)[/tex]
2.
Completely factored states that an expression is completely factored when no further factor is possible.
C.
[tex]24x^6-18x^5[/tex]
Take greatest common factor out [tex]6x^5[/tex];
[tex]6x^5(4x-3)[/tex]
[tex]24x^6-18x^5 =6x^5(4x-3) [/tex]
D.
[tex]20x^3+12x^2[/tex]
Take greatest common factor out [tex]4x^2[/tex];
[tex]4x^2(5x+3)[/tex]
[tex]20x^3+12x^2 =4x^2(5x+3)[/tex]
Therefore, Only option C and D expressions are completely factored.
