Combining Like Terms
4x + 5x=9x\\2y+4x+5y+3x=7y+7x\\3x+5+6x=9x+5
Combining like terms with negative coefficients & distribution
2(3x+5)\\=(2)(3x)+(2)(5)\\=6x+10
7(3y-5)-2(10+4y)=\\=21y-35-20-8y\\=(21y-8y)(-35-20)\,grouped\\=13y-55
We group same terms. We use the precedent when noting negative or positive.
Combining like terms with negative coefficients
Note y is different y2. They cannot be added nor subtracted.
-3y+4xy-2x^2+2x+y^2-4xy+2y+3x^2\\=[-3y+2y]\cancel{[4xy-4xy]}[-2x^2+3x^2]+2x+y^2\\=-y+x^2+2x+y^2-k\cancel-(\cancel-8k)\\=-k+8k\\=7k
Combining like terms with rational coefficients
-5.55-8.55c+4.35c\\=-5.55[-8.55c+4.35c]\\=-5.55-4.2c
\frac{2}{5}m-\frac{4}{5}-\frac{3}{5}m\\=[\frac{2}{5}m-\frac{3}{5}m]-\frac{4}{5}\\=-\frac{1}{5}m-\frac{4}{5}2(\frac{1}{5}m-\frac{2}{5})+\frac{3}{5}\\=\frac{2}{5}m[-\frac{4}{5}+\frac{3}{5}]\\=\frac{2}{5}m-\frac{1}{5}