expand piΔ(x+Δx)^2

الحلّ

expand

π Δ (x + Δ x)^{2}

π Δ x^{2} + 2 Δ^{2} π x^{2} + Δ^{3} π x^{2}

خطوات الحلّ

π Δ (x + Δ x)^{2}

(x + Δ x)^{2} = x^{2} + 2Δ x^{2} + Δ^{2} x^{2}

= π Δ (x^{2} + 2Δ x^{2} + Δ^{2} x^{2})

فعّل قانون ضرب الأقواس

= π Δ x^{2} + π Δ2Δ x^{2} + π Δ Δ^{2} x^{2}

= π Δ x^{2} + 2 π ΔΔ x^{2} + Δ^{2} π Δ x^{2}

π Δ x^{2} + 2 π ΔΔ x^{2} + Δ^{2} π Δ x^{2}

بسّط:

π Δ x^{2} + 2 Δ^{2} π x^{2} + Δ^{3} π x^{2}

= π Δ x^{2} + 2 Δ^{2} π x^{2} + Δ^{3} π x^{2}

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