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