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Which expression is equivalent to this polynomial expression? (5xy^2 + 3x^2 – 7) + (3x^2y^2 – xy^2 + 3y^2 + 4) A. 3.x^2y^2 + 4xy^2 + 3x^2 + 3y^2 – 3 B. 9x^2y^2 + 4xy^2 – 3 C. 3x^2y^2 + 6xy^2 + 6x^2 + 3 D. 8x^2y^2 + 2xy^2 - 4y^2 + 4

Respuesta :

According to the given data we have the following polynomial expression:

(5xy^2 + 3x^2 – 7) + (3x^2y^2 – xy^2 + 3y^2 + 4)

To find out which expression is equivalent to the one above, we woule have to make the following calculation:

First:

[tex]\mathrm{Remove\: parentheses}\colon\quad \mleft(a\mright)=a[/tex][tex]=5xy^2+3x^2-7+3x^2y^2-xy^2+3y^2+4[/tex]

Next, group like terms:

[tex]=3x^2y^2+3x^2+5xy^2-xy^2+3y^2-7+4[/tex]

Next, add similar elements:

[tex]3x^2y^2+3x^2+4xy^2+3y^2-7+4[/tex][tex]\mathrm{Add/Subtract\: the\: numbers\colon}\: -7+4=-3[/tex]

So we would get the following equivalent expression:

[tex]=3x^2y^2+3x^2+4xy^2+3y^2-3[/tex]

Therefore, the right option would be A.

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