# Simplify combining like terms:$(i)$. $21b-32+7b-20b$$(ii). -z^2+13z^2-5z+7z^3-15z$$(iii)$. $p-(p-q)-q-(q-p)$$iv). 3a-2b-ab-(a-b+ab)+3ab+b-a$$(v)$. $5x^2y-5x^2+3yx^2-3y^2+x^2-y^2+8xy^2-3y^2$$(vi)$. $(3y2+5y-4)-(8y-y2-4)$

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Given: $(i)$. $21b-32+7b-20b$

$(ii)$. $-z^2+13z^2-5z+7z^3-15z$

$(iii)$. $p-(p-q)-q-(q-p)$

$iv)$. $3a-2b-ab-(a-b+ab)+3ab+b-a$

$(v)$. $5x^2y-5x^2+3yx^2-3y^2+x^2-y^2+8xy^2-3y^2$

$(vi)$. $(3y^2+5y-4)-(8y-y^2-4)$

To do: To simplify combining like terms.

Solution:

$(i)$ $21b-32+7b-20b$

$=21b+7b-20b-32$             [On arranging like terms]

$=b(21+7-20)-32$

$=8b-32$

$(ii)$ $-z^2+13z^2-5z+7z^3-15z$

$=7z^{3}+z^2+13z^2-5z+5z-15z$      [On arranging like terms]

$=7z^3+(-1+13)z^2+(-5-15)z$

$= 7z^3 + 12z^2 – 20z$

$(iii)$ $p-(p-q)-q-(q-p)$

$=p-p+q-q-q+p$                 [On arranging like terms]

$=p-q$

$(iv)$ $3a-2b-ab-(a-b+ab)+3ab+b-a$

$=3a-2b-ab-a+b-ab+3ab+b-a$             [On arranging like terms]

$=3a-a-a-2b+b+b-ab-ab+3ab$

$=3a-2a-2ab+3ab$

$=a+ab$

$(v)$ $5x^2y-5x^2+3yx^2-3y^2+x^2-y^2+8xy^2-3y^2$

$=5x^2y+3x^2y+8xy^2-5x^{2}+x^{2}-3y^2-y^2-3y^2$    [On arranging like terms]

$=8x^2y+8xy^2-4x^2-7y^2$

$(vi)$. $(3y^2+5y-4)-(8y-y^2-4)$

$=3y^2+5y-4-8y+y^2+4$        [On arranging like terms]

$=4y^{2}-3y$

Updated on 10-Oct-2022 13:38:20