Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((p+6)(p+6)=(p+6)^2=p^2+\color{magenta}{2.p.6}+6^2=p^2\color{magenta}{+12p}+36\)
2. \((x-11)(x-11)=(x-11)^2=x^2+\color{magenta}{2.x.(-11)}+(-11)^2=x^2\color{magenta}{-22x}+121\)
3. \((\color{blue}{-5s^2}\color{red}{+14})(\color{blue}{-5s^2}\color{red}{-14})=\color{blue}{(-5s^2)}^2-\color{red}{14}^2=25s^{4}-196\)
4. \((-8a-9)(-8a-9)=(-8a-9)^2=(-8a)^2+\color{magenta}{2.(-8a).(-9)}+(-9)^2=64a^2\color{magenta}{+144a}+81\)
5. \((\color{blue}{s}\color{red}{-14})(\color{blue}{s}\color{red}{+14})=\color{blue}{s}^2-\color{red}{14}^2=s^2-196\)
6. \((\color{red}{-4p}\color{blue}{-2})(\color{red}{4p}\color{blue}{-2})=\color{blue}{(-2)}^2-\color{red}{(4p)}^2=4-16p^2\)
7. \((-2a^2+13)(-2a^2+13)=(-2a^2+13)^2=(-2a^2)^2\color{magenta}{+2.(-2a^2).13}+13^2=4a^{4}\color{magenta}{-52a^2}+169\)
8. \((\color{blue}{7x^2}\color{red}{+1})(\color{blue}{7x^2}\color{red}{-1})=\color{blue}{(7x^2)}^2-\color{red}{1}^2=49x^{4}-1\)
9. \((3s^4-2)(3s^4-2)=(3s^4-2)^2=(3s^4)^2\color{magenta}{+2.(3s^4).(-2)}+(-2)^2=9s^{8}\color{magenta}{-12s^4}+4\)
10. \((\color{red}{15a}\color{blue}{-14})(\color{red}{-15a}\color{blue}{-14})=\color{blue}{(-14)}^2-\color{red}{(15a)}^2=196-225a^2\)
11. \((\color{blue}{11s^4}\color{red}{+8})(\color{blue}{11s^4}\color{red}{-8})=\color{blue}{(11s^4)}^2-\color{red}{8}^2=121s^{8}-64\)
12. \((\color{blue}{x}\color{red}{-7})(\color{blue}{x}\color{red}{+7})=\color{blue}{x}^2-\color{red}{7}^2=x^2-49\)