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Sagot :
GIVEN:
We are given the polynomials below;
[tex](6x^2-3x-6)(4x^2+5x+4)[/tex]Required;
To determine the product of the polynomials given.
Step-by-step solution;
We shall multiply the terms in parenthesis by distributing the terms on the left among the ones on the right one after the other as shown below;
[tex]\begin{gathered} 6x^2\times(4x^2+5x+4) \\ \\ -3x\times(4x^2+5x+4) \\ \\ -6\times(4x^2+5x+4) \end{gathered}[/tex]We can now simplify as follows;
[tex]24x^4+30x^3+24x^2-12x^3-15x^2-12x-24x^2-30x-24[/tex]Next step, we collect all like terms;
[tex]\begin{gathered} 24x^4+30x^3-12x^3+24x^2-24x^2-15x^2-12x-30x-24 \\ \\ =24x^4+18x^3-15x^2-42x-24 \end{gathered}[/tex]Therefore, the product of the polynomials
ANSWER:
[tex]24x^4+18x^3-15x^2-42x-24[/tex]
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