Factorise :
a2+bc−ac−b2a^2 + bc - ac - b^2a2+bc−ac−b2
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a2+bc−ac−b2=(a2−b2)+(bc−ac)=(a−b)(a+b)+(bc−ac)=(a−b)(a+b)+c(b−a)=−(b−a)(a+b)+c(b−a)=(b−a)[−(a+b)+c]=(b−a)[−a−b+c]=(a−b)(a+b−c)a^2 + bc - ac - b^2 = (a^2 - b^2) + (bc - ac)\\[1em] = (a - b)(a + b) + (bc - ac)\\[1em] = (a - b)(a + b) + c(b - a)\\[1em] = -(b - a)(a + b) + c(b - a)\\[1em] = (b - a)[-(a + b) + c]\\[1em] = (b - a)[- a - b + c]\\[1em] = (a - b)(a + b - c)a2+bc−ac−b2=(a2−b2)+(bc−ac)=(a−b)(a+b)+(bc−ac)=(a−b)(a+b)+c(b−a)=−(b−a)(a+b)+c(b−a)=(b−a)[−(a+b)+c]=(b−a)[−a−b+c]=(a−b)(a+b−c)
Hence, a2+bc−ac−b2=(a−b)(a+b−c)a^2 + bc - ac - b^2 = (a - b)(a + b - c)a2+bc−ac−b2=(a−b)(a+b−c).
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