Automatismes

Développement - Exercice 2

1 min
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Question 1

A=(2x+1)(x1)+(3x1)(x+3)A=\left(2x+1\right)\left(x-1\right)+\left(3x-1\right)\left(x+3\right)

Correction
A=(2x+1)(x1)+(3x1)(x+3)A={\color{brown}\left(2x+1\right)\left(x-1\right)}+{\color{green}\left(3x-1\right)\left(x+3\right)}
A=2x×x+2x×(1)+1×x+1×(1)+3x×x+3x×3+(1)×x+(1)×3A={\color{brown}2x\times x+2x\times \left(-1\right)+1\times x+1\times \left(-1\right)}+{\color{green}3x\times x+3x\times 3+\left(-1\right)\times x+\left(-1\right)\times 3}
A=2x22x+x1+3x2+9xx3A=2x^{2} -2x+x-1+3x^{2} +9x-x-3
A=2x2+3x22x+x+9xx13A=2x^{2} +3x^{2} -2x+x+9x-x-1-3
A=5x2+7x4\color{blue}A=5x^{2} +7x-4
Question 2

B=(x+7)29B =(x+7)^2-9

Correction
  • (a+b)2=a2+2ab+b2\left({\color{blue}a}+{\color{red}b}\right)^{2} ={\color{blue}a}^{2} +2{\color{blue}a}{\color{red}b}+{\color{red}b}^{2}

B=(x+7)29B={\color{brown}(x+7)^2}-9 équivaut successivement à :
B=(x2+2×x×7+72)9B={\color{brown}(x^2+2\times{x}\times{7}+7^2)}-9
B=(x2+14x+49)9B={\color{brown}(x^2+14x+49)}-9
B=x2+14x+499B=x^2+14x+49-9
B=x2+14x+40\color{blue}B=x^{2} +14x+40
Question 3

C=(2x+5)(x5)+(5x1)(x2)C=\left(2x+5\right)\left(x-5\right)+\left(5x-1\right)\left(x-2\right)

Correction
C=(2x+5)(x5)+(5x1)(x2)C={\color{brown}\left(2x+5\right)\left(x-5\right)}+{\color{green}\left(5x-1\right)\left(x-2\right)} équivaut successivement à :
C=2x×x+2x×(5)+5×x+5×(5)+5x×x+5x×(2)+(1)×x+(1)×(2)C={\color{brown}2x\times x+2x\times \left(-5\right)+5\times x+5\times \left(-5\right)}+{\color{green}5x\times x+5x\times \left(-2\right)+\left(-1\right)\times x+\left(-1\right)\times \left(-2\right)}
C=2x210x+5x25+5x210xx+2C=2x^{2} -10x+5x-25+5x^{2} -10x-x+2
C=7x216x23\color{blue}C=7x^{2} -16x-23