Middle School

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------------------------------------------------ Simplify the expression [tex]3(x + 2)(x^2 − x − 8)[/tex].

A. [tex]3x^3 + 3x^2 − 30x − 48[/tex]
B. [tex]3x^3 + x^2 − 10x − 16[/tex]
C. [tex]3x^3 − 30x^2 − 12x − 48[/tex]
D. [tex]3x^3 − 4x^2 − 30x − 4[/tex]

Answer :

Answer:

The correct option is A) [tex]3x^3+3x^2-30x-48[/tex]

Step-by-step explanation:

Consider the provided expression.

[tex]3\left(x+2\right)\left(x^2-x-8\right)[/tex]

Distribute 3 as shown

[tex]\left(3x+6\right)\left(x^2-x-8\right)[/tex]

Distribute parentheses as shown.

[tex]3xx^2+3x\left(-x\right)+3x\left(-8\right)+6x^2+6\left(-x\right)+6\left(-8\right)[/tex]

[tex]3x^2x-3xx-3\cdot \:8x+6x^2-6x-6\cdot \:8[/tex]

[tex]3x^3-3x^2-24x+6x^2-6x-48[/tex]

Add and subtract like terms

[tex]3x^3+3x^2-30x-48[/tex]

Hence, the correct option is A) [tex]3x^3+3x^2-30x-48[/tex]

Answer:

3x^3 + 3x^2 − 30x − 48

Step-by-step explanation:

3( x + 2 )( x^2 − x − 8 )

= ( 3( x + 2 ))( x^2 + − x + − 8 )

= ( 3( x + 2 ))( x^2 ) + ( 3( x + 2 ))( −x ) + ( 3( x + 2 ))( −8 )

= 3x^3 + 6x^2 − 3x^2 − 6x − 24x − 48

3x^3 + 3x^2 − 30x − 48