Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

1. \((-b^3-5)(-b^3+5)\)
2. \((9b^4+6)(9b^4+6)\)
3. \((s+14)(s-14)\)
4. \((a-11)(a+11)\)
5. \((10y^5+3)(-10y^5+3)\)
6. \((y-11)^2\)
7. \((-2p^2-3b)(-2p^2-3b)\)
8. \((13s^5+4)^2\)
9. \((2b+8)(-2b+8)\)
10. \((5x^2+2)(5x^2+2)\)
11. \((4b-1)(4b+1)\)
12. \((16y^5-2s)(16y^5+2s)\)

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{blue}{-b^3}\color{red}{-5})(\color{blue}{-b^3}\color{red}{+5})=\color{blue}{(-b^3)}^2-\color{red}{(-5)}^2=b^{6}-25\)
2. \((9b^4+6)(9b^4+6)=(9b^4+6)^2=(9b^4)^2\color{magenta}{+2.(9b^4).6}+6^2=81b^{8}\color{magenta}{+108b^4}+36\)
3. \((\color{blue}{s}\color{red}{+14})(\color{blue}{s}\color{red}{-14})=\color{blue}{s}^2-\color{red}{14}^2=s^2-196\)
4. \((\color{blue}{a}\color{red}{-11})(\color{blue}{a}\color{red}{+11})=\color{blue}{a}^2-\color{red}{11}^2=a^2-121\)
5. \((\color{red}{10y^5}\color{blue}{+3})(\color{red}{-10y^5}\color{blue}{+3})=\color{blue}{3}^2-\color{red}{(10y^5)}^2=9-100y^{10}\)
6. \((y-11)^2=y^2+\color{magenta}{2.y.(-11)}+(-11)^2=y^2\color{magenta}{-22y}+121\)
7. \((-2p^2-3b)(-2p^2-3b)=(-2p^2-3b)^2=(-2p^2)^2\color{magenta}{+2.(-2p^2).(-3b)}+(-3b)^2=4p^{4}\color{magenta}{+12bp^2}+9b^2\)
8. \((13s^5+4)^2=(13s^5)^2\color{magenta}{+2.(13s^5).4}+4^2=169s^{10}\color{magenta}{+104s^5}+16\)
9. \((\color{red}{2b}\color{blue}{+8})(\color{red}{-2b}\color{blue}{+8})=\color{blue}{8}^2-\color{red}{(2b)}^2=64-4b^2\)
10. \((5x^2+2)(5x^2+2)=(5x^2+2)^2=(5x^2)^2\color{magenta}{+2.(5x^2).2}+2^2=25x^{4}\color{magenta}{+20x^2}+4\)
11. \((\color{blue}{4b}\color{red}{-1})(\color{blue}{4b}\color{red}{+1})=\color{blue}{(4b)}^2-\color{red}{(-1)}^2=16b^2-1\)
12. \((\color{blue}{16y^5}\color{red}{-2s})(\color{blue}{16y^5}\color{red}{+2s})=\color{blue}{(16y^5)}^2-\color{red}{(-2s)}^2=256y^{10}-4s^2\)