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Choose the correct simplification of [tex](4x - 3)(3x^2 - 4x - 3)[/tex].

A. [tex]12x^3 + 25x^2 + 9[/tex]
B. [tex]12x^3 - 25x^2 - 9[/tex]
C. [tex]12x^3 + 25x^2 - 9[/tex]
D. [tex]12x^3 - 25x^2 + 9[/tex]

Answer :

Answer:

[tex]12x^{3}-25x^{2}+9[/tex]

Step-by-step explanation:

1. Write down the equation:

[tex](4x-3)(3x^{2}-4x-3)[/tex]

2. Multiply the first term on the left parenthesis by each term on the right parenthesis:

[tex]4x*3x^{2}=12x^{3}[/tex]

[tex]4x*(-4x)=-16x^{2}[/tex]

[tex]4x*(-3)=-12x[/tex]

3. Multiply the second term on the left parenthesis by each term on the right parenthesis:

[tex]-3*(3x^{2})=-9x^{2}[/tex]

[tex]-3*(-4x)=12x[/tex]

[tex]-3*(-3)=9[/tex]

4. Add up all the terms:

[tex]12x^{3}-16x^{2}-12x-9x^{2}+12x+9[/tex]

Simplify:

[tex]12x^{3}-25x^{2}+9[/tex]

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Rewritten by : Barada

Answer: [tex]12x^3-25x^2+9[/tex]

Step-by-step explanation:

Given expression: [tex](4x-3)(3x^2-4x-3)[/tex]

To simplify the above expression we apply the distributive property [ (b+c)a=ba+ca, where a,b, c be any expression] we get ,

[tex](4x-3)(3x^2-4x-3)\\\\=4x(3x^2-4x-3)-3(3x^2-4x-3)\\\\=12x^{1+2}-16x^{1+1}-12x-9x^2+12x+9.......\text{[by law of exponents]}\\\\=12x^{3}-16x^{2}-12x-9x^2+12x+9\\\\\text{Combing like terms, we get}\\\\=12x^3-(16+9)x^2-12x+12x+9\\\\=12x^3-25x^2+9[/tex]