Respuesta :
For multiplying two polynomials, we will multiply each term in the first parenthesis with the whole second parenthesis part and then use distributive property and simplify in the end.
Polynomial product A
[tex](4x^2 -4x)(x^2 -4)\\ \\ =4x^2(x^2-4)-4x(x^2-4)\\ \\ = 4x^4-16x^2-4x^3+16x\\ \\ =4x^4-4x^3-16x^2+16x[/tex]
Polynomial product B
[tex](x^2+x-2)(4x^2-8x)\\ \\ =x^2(4x^2-8x)+x(4x^2-8x)-2(4x^2-8x)\\ \\ =4x^4-8x^3+4x^3-8x^2-8x^2+16x\\ \\=4x^4-4x^3-16x^2+16x[/tex]
Thus, the products of the two polynomials are the same.
Answer:
We need to multiply of given polynomials
Given:-
Polynomial product A : [tex](4x^{2}-4x)(x^{2}-4)[/tex]
Polynomial product B : [tex](x^{2}+x-2)(4x^{2}-8x)[/tex]
For product A : [tex](4x^{2}-4x)(x^{2}-4)[/tex]
multiply term wise,
[tex]4x^{2}(x^{2}-4)-4x(x^{2}-4)[/tex]
[tex]4x^{2+2}-4\times 4x^{2}-4x^{2+1}+4\times 4x[/tex]
[tex]4x^{4}-16x^{2}-4x^{3}+16x[/tex]
[tex]4x^{4}-4x^{3}-16x^{2}+16x[/tex]
For product B : [tex](x^{2}+x-2)(4x^{2}-8x)[/tex]
multiply term wise,
[tex]x^{2}(4x^{2}-8x)+x(4x^{2}-8x)-2(4x^{2}-8x)[/tex]
[tex]4x^{2+2}-8x^{2+1}+4x^{2+1}-8x^{1+1}-8x^{2}+16x[/tex]
[tex]4x^{4}-4x^{3}-8x^{2}-16x^{2}+16x[/tex]
Therefore, the products of the two polynomials are the same
