Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((q-15)^2=q^2+\color{magenta}{2.q.(-15)}+(-15)^2=q^2\color{magenta}{-30q}+225\)
2. \((14y^3+12p)(14y^3+12p)=(14y^3+12p)^2=(14y^3)^2\color{magenta}{+2.(14y^3).(12p)}+(12p)^2=196y^{6}\color{magenta}{+336py^3}+144p^2\)
3. \((\color{blue}{y}\color{red}{-7})(\color{blue}{y}\color{red}{+7})=\color{blue}{y}^2-\color{red}{7}^2=y^2-49\)
4. \((\color{blue}{-13p^4}\color{red}{+12b})(\color{blue}{-13p^4}\color{red}{-12b})=\color{blue}{(-13p^4)}^2-\color{red}{(12b)}^2=169p^{8}-144b^2\)
5. \((p^3+2)^2=(p^3)^2\color{magenta}{+2.(p^3).2}+2^2=1p^{6}\color{magenta}{+4p^3}+4\)
6. \((8y-16)(8y-16)=(8y-16)^2=(8y)^2+\color{magenta}{2.(8y).(-16)}+(-16)^2=64y^2\color{magenta}{-256y}+256\)
7. \((\color{red}{4y}\color{blue}{+11})(\color{red}{-4y}\color{blue}{+11})=\color{blue}{11}^2-\color{red}{(4y)}^2=121-16y^2\)
8. \((y-5)^2=y^2+\color{magenta}{2.y.(-5)}+(-5)^2=y^2\color{magenta}{-10y}+25\)
9. \((-6p^3-3q)^2=(-6p^3)^2\color{magenta}{+2.(-6p^3).(-3q)}+(-3q)^2=36p^{6}\color{magenta}{+36p^3q}+9q^2\)
10. \((-3s^4-8b)(-3s^4-8b)=(-3s^4-8b)^2=(-3s^4)^2\color{magenta}{+2.(-3s^4).(-8b)}+(-8b)^2=9s^{8}\color{magenta}{+48bs^4}+64b^2\)
11. \((\color{blue}{a}\color{red}{+15})(\color{blue}{a}\color{red}{-15})=\color{blue}{a}^2-\color{red}{15}^2=a^2-225\)
12. \((-4s^4-8)^2=(-4s^4)^2\color{magenta}{+2.(-4s^4).(-8)}+(-8)^2=16s^{8}\color{magenta}{+64s^4}+64\)