Cours Développer, identitiés remarquables

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Question 1

$(x+2)^2=$

$x^2+2x+2$

$x^2+2x+4$

$x^2+4x+4$

$(x+2)^2=x^2+2\times x\times 2+2^2$

$(x+2)^2=x^2+4x+4$

Question 2

$(3x+1)^2=$

$3x^2+3x+1$

$9x^2+6x+1$

$(3x+1)^2=(3x)^2+2\times 3x\times 1+1^2$

$(3x+1)^2=9x^2+6x+1$

$3x^2+6x+1$

Question 3

$(x-5)(x+5)=$

$x^2-25$

$(x-5)(x+5)=(x)^2-(5)^2$

$(x-5)(x+5)=x^2-25$

$5x^2-25$

$x^2-5$

Question 4

$(x-4)^2=$

$x^2-16x-16$

$x^2-16x+16$

$x^2-8x+16$

$(x-4)^2=x^2-2\times x\times 4+4^2$

$(x-4)^2=x^2-8x+16$

Question 5

$(3x-5)(3x+5)=$

$9x^2-25$

$(3x-5)(3x+5)=(3x)^2-(5)^2$

$(3x-5)(3x+5)=9x^2-25$

$3x^2-25$

$9x^2+25$

Question 6

$(3x-4)^2=$

$3x^2-24x+16$

$9x^2+24x+16$

$9x^2-24x+16$

$(3x-4)^2=(3x)^2-2\times 3x\times 4+4^2$

$(3x-4)^2=9x^2-24x+16$

Question 7

$(6x+1)(6x-1)=$

$36x^2-1$

$(6x+1)(6x-1)=(6x)^2-(1)^2$

$(6x+1)(6x-1)=36x^2-1$

$36x^2+12x+1$

$36x^2-12x+1$

Question 8

$(0,1x + 10)^2=$

$100x^2+2x+0,01$

$0,01x^2+2x+100$

$(0,1x + 10)^2=(0,1x)^2+2\times 0,1x\times10 +10^2$

$(0,1x + 10)^2=0,01x^2+2x+100$

$0,01x^2+x+100$

Question 9

$(0,05x - 10)^2=$

$0,0025x^2-x+100$

$(0,05x - 10)^2=(0,05x)^2-2\times 0,05x\times10+10^2$

$(0,05x - 10)^2=0,0025x^2-x+100$

$0,025x^2-x+100$

$0,0025x^2-5x+100$

Question 10

$\left(3x+\dfrac{2}{5}\right)^2=$

$9x^2+\dfrac{12}{5}x+\dfrac{4}{25}$

$\left(3x+\dfrac{2}{5}\right)^2=(3x)^2+2 \times 3x\times \dfrac{2}{5}+\left(\dfrac{2}{5}\right)^2$

$\left(3x+\dfrac{2}{5}\right)^2=9x^2+\dfrac{12}{5}x+\dfrac{4}{25}$

$9x^2+\dfrac{12}{5}x+\dfrac{2}{5}$

$9x^2+\dfrac{6}{5}x+\dfrac{4}{25}$