Expansion of (x ± a)(x ± b)

We will discuss here about the expansion of (x ± a)(x ± b)

(x + a)(x + b) = x(x + b) + a (x + b)

                      = x\(^{2}\) + xb + ax + ab

                      = x\(^{2}\) + (b + a)x + ab


(x - a)(x - b) = x(x - b) - a (x - b)

                    = x\(^{2}\) - xb - ax + ab

                    = x\(^{2}\) - (b + a)x + ab





(x + a)(x - b) = x(x - b) + a (x - b)

                     = x\(^{2}\) - xb + ax - ab

                     = x\(^{2}\) + (a - b)x - ab


(x - a)(x + b) = x(x + b) - a (x + b)

                     = x\(^{2}\) + xb - ax - ab

                     = x\(^{2}\) - (a - b)x – ab


Thus, we have

(x + a)(x + b) = x\(^{2}\) + (b + a)x + ab

(x - a)(x - b) = x\(^{2}\) - (b + a)x + ab

(x + a)(x - b) = x\(^{2}\) + (a - b)x - ab

(x - a)(x + b) = x\(^{2}\) - (a - b)x – ab

(x + a)(x + b) = x\(^{2}\) + (Sum of constant terms)x + Product of constant terms.










9th Grade Math

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