Question

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

Answer 1

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:

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

Next, group like terms:

`=3x^2y^2+3x^2+5xy^2-xy^2+3y^2-7+4`

Next, add similar elements:

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

So we would get the following equivalent expression:

`=3x^2y^2+3x^2+4xy^2+3y^2-3`

Therefore, the right option would be A.