Factorise :
a2−b2−c2+2bca^2 - b^2 - c^2 + 2bca2−b2−c2+2bc
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a2−b2−c2+2bc=a2−(b2+c2−2bc)=a2−(b−c)2=[a−(b−c)][a+(b−c)]=(a−b+c)(a+b−c)a^2 - b^2 - c^2 + 2bc = a^2 - (b^2 + c^2 - 2bc)\\[1em] = a^2 - (b - c)^2\\[1em] = [a - (b - c)][a + (b - c)]\\[1em] = (a - b + c)(a + b - c)a2−b2−c2+2bc=a2−(b2+c2−2bc)=a2−(b−c)2=[a−(b−c)][a+(b−c)]=(a−b+c)(a+b−c)
Hence, b2+c2+2bc−a2b^2 + c^2 + 2bc - a^2b2+c2+2bc−a2 = (a - b + c)(a + b - c).
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If x - y = 7 and x3−y3=133;x^3 - y^3 = 133;x3−y3=133; find :
(i) xy
(ii) x2+y2x^2 + y^2x2+y2
b2+c2+2bc−a2b^2 + c^2 + 2bc - a^2b2+c2+2bc−a2
a+2b+a3+8b3a + 2b + a^3 + 8b^3a+2b+a3+8b3
x2−8xx^2 - \dfrac{8}{x}x2−x8
