Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((-16x^3+10s)^2=(-16x^3)^2\color{magenta}{+2.(-16x^3).(10s)}+(10s)^2=256x^{6}\color{magenta}{-320sx^3}+100s^2\)
2. \((6s^5+10)(6s^5+10)=(6s^5+10)^2=(6s^5)^2\color{magenta}{+2.(6s^5).10}+10^2=36s^{10}\color{magenta}{+120s^5}+100\)
3. \((q-8)^2=q^2+\color{magenta}{2.q.(-8)}+(-8)^2=q^2\color{magenta}{-16q}+64\)
4. \((\color{blue}{-7p^2}\color{red}{+15y})(\color{blue}{-7p^2}\color{red}{-15y})=\color{blue}{(-7p^2)}^2-\color{red}{(15y)}^2=49p^{4}-225y^2\)
5. \((q+8)(q+8)=(q+8)^2=(q)^2+\color{magenta}{2.(q).8}+8^2=q^2\color{magenta}{+16q}+64\)
6. \((\color{blue}{y}\color{red}{-8})(\color{blue}{y}\color{red}{+8})=\color{blue}{y}^2-\color{red}{8}^2=y^2-64\)
7. \((\color{blue}{-10y}\color{red}{+6})(\color{blue}{-10y}\color{red}{-6})=\color{blue}{(-10y)}^2-\color{red}{(6)}^2=100y^2-36\)
8. \((3x^5+15)(3x^5+15)=(3x^5+15)^2=(3x^5)^2\color{magenta}{+2.(3x^5).15}+15^2=9x^{10}\color{magenta}{+90x^5}+225\)
9. \((-11a^2-4)^2=(-11a^2)^2\color{magenta}{+2.(-11a^2).(-4)}+(-4)^2=121a^{4}\color{magenta}{+88a^2}+16\)
10. \((a^3-11)^2=(a^3)^2\color{magenta}{+2.(a^3).(-11)}+(-11)^2=1a^{6}\color{magenta}{-22a^3}+121\)
11. \((x+15)^2=x^2+\color{magenta}{2.x.15}+15^2=x^2\color{magenta}{+30x}+225\)
12. \((\color{blue}{b}\color{red}{+2})(\color{blue}{b}\color{red}{-2})=\color{blue}{b}^2-\color{red}{2}^2=b^2-4\)