Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((-16a^4-1)(-16a^4-1)=(-16a^4-1)^2=(-16a^4)^2\color{magenta}{+2.(-16a^4).(-1)}+(-1)^2=256a^{8}\color{magenta}{+32a^4}+1\)
2. \((y+1)^2=y^2+\color{magenta}{2.y.1}+1^2=y^2\color{magenta}{+2y}+1\)
3. \((-11s^5+6)(-11s^5+6)=(-11s^5+6)^2=(-11s^5)^2\color{magenta}{+2.(-11s^5).6}+6^2=121s^{10}\color{magenta}{-132s^5}+36\)
4. \((-8y^3-11)(-8y^3-11)=(-8y^3-11)^2=(-8y^3)^2\color{magenta}{+2.(-8y^3).(-11)}+(-11)^2=64y^{6}\color{magenta}{+176y^3}+121\)
5. \((\color{red}{-16p^2}\color{blue}{+2q})(\color{red}{16p^2}\color{blue}{+2q})=\color{blue}{(2q)}^2-\color{red}{(16p^2)}^2=4q^2-256p^{4}\)
6. \((x+8)^2=x^2+\color{magenta}{2.x.8}+8^2=x^2\color{magenta}{+16x}+64\)
7. \((-4s^3+7q)(-4s^3+7q)=(-4s^3+7q)^2=(-4s^3)^2\color{magenta}{+2.(-4s^3).(7q)}+(7q)^2=16s^{6}\color{magenta}{-56qs^3}+49q^2\)
8. \((7b-13)(7b-13)=(7b-13)^2=(7b)^2+\color{magenta}{2.(7b).(-13)}+(-13)^2=49b^2\color{magenta}{-182b}+169\)
9. \((\color{red}{6y}\color{blue}{-4})(\color{red}{-6y}\color{blue}{-4})=\color{blue}{(-4)}^2-\color{red}{(6y)}^2=16-36y^2\)
10. \((\color{blue}{-16s^2}\color{red}{-14})(\color{blue}{-16s^2}\color{red}{+14})=\color{blue}{(-16s^2)}^2-\color{red}{(-14)}^2=256s^{4}-196\)
11. \((\color{blue}{x}\color{red}{-14})(\color{blue}{x}\color{red}{+14})=\color{blue}{x}^2-\color{red}{14}^2=x^2-196\)
12. \((a-15)^2=(a)^2+\color{magenta}{2.(a).(-15)}+(-15)^2=a^2\color{magenta}{-30a}+225\)