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(y^2+5y-7)-(y^2-3y-4)

$\begin{array}{rcll} (y^2+5y-7)-(y^2-3y-4) &=&\\ &=& y^2+5y-7-(y^2-3y-4)\\ &=& y^2+5y-7-y^2+3y+4\\ &=& y^2-y^2+5y+3y-7+4 \qquad & | \qquad y^2-y^2 = 0\\ &=& 5y+3y-7+4 \qquad & | \qquad 5y+3y= 8y\\ &=& 8y-7+4 \qquad & | \qquad-7+4 =-3\\ &=& 8y-3 \\ \mathbf{(y^2+5y-7)-(y^2-3y-4)} &\mathbf{=}& \mathbf{8y-3 } \end{array}$