Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

1. \((x-5)(x+5)\)
2. \((p+1)(p-1)\)
3. \((y+7)(y+7)\)
4. \((-8b^2-3s)(-8b^2-3s)\)
5. \((b-2)(b+2)\)
6. \((-14a^2+7)(-14a^2-7)\)
7. \((16x-15)(16x+15)\)
8. \((-4s^4+3)(4s^4+3)\)
9. \((-13y^3-7p)(-13y^3+7p)\)
10. \((p-10)(p+10)\)
11. \((-12x^2-15)(-12x^2+15)\)
12. \((-16p+5)(16p+5)\)

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{blue}{x}\color{red}{-5})(\color{blue}{x}\color{red}{+5})=\color{blue}{x}^2-\color{red}{5}^2=x^2-25\)
2. \((\color{blue}{p}\color{red}{+1})(\color{blue}{p}\color{red}{-1})=\color{blue}{p}^2-\color{red}{1}^2=p^2-1\)
3. \((y+7)(y+7)=(y+7)^2=y^2+\color{magenta}{2.y.7}+7^2=y^2\color{magenta}{+14y}+49\)
4. \((-8b^2-3s)(-8b^2-3s)=(-8b^2-3s)^2=(-8b^2)^2\color{magenta}{+2.(-8b^2).(-3s)}+(-3s)^2=64b^{4}\color{magenta}{+48b^2s}+9s^2\)
5. \((\color{blue}{b}\color{red}{-2})(\color{blue}{b}\color{red}{+2})=\color{blue}{b}^2-\color{red}{2}^2=b^2-4\)
6. \((\color{blue}{-14a^2}\color{red}{+7})(\color{blue}{-14a^2}\color{red}{-7})=\color{blue}{(-14a^2)}^2-\color{red}{7}^2=196a^{4}-49\)
7. \((\color{blue}{16x}\color{red}{-15})(\color{blue}{16x}\color{red}{+15})=\color{blue}{(16x)}^2-\color{red}{(-15)}^2=256x^2-225\)
8. \((\color{red}{-4s^4}\color{blue}{+3})(\color{red}{4s^4}\color{blue}{+3})=\color{blue}{3}^2-\color{red}{(4s^4)}^2=9-16s^{8}\)
9. \((\color{blue}{-13y^3}\color{red}{-7p})(\color{blue}{-13y^3}\color{red}{+7p})=\color{blue}{(-13y^3)}^2-\color{red}{(-7p)}^2=169y^{6}-49p^2\)
10. \((\color{blue}{p}\color{red}{-10})(\color{blue}{p}\color{red}{+10})=\color{blue}{p}^2-\color{red}{10}^2=p^2-100\)
11. \((\color{blue}{-12x^2}\color{red}{-15})(\color{blue}{-12x^2}\color{red}{+15})=\color{blue}{(-12x^2)}^2-\color{red}{(-15)}^2=144x^{4}-225\)
12. \((\color{red}{-16p}\color{blue}{+5})(\color{red}{16p}\color{blue}{+5})=\color{blue}{5}^2-\color{red}{(16p)}^2=25-256p^2\)