Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((-16s-8)^2=(-16s)^2+\color{magenta}{2.(-16s).(-8)}+(-8)^2=256s^2\color{magenta}{+256s}+64\)
2. \((\color{blue}{10p^3}\color{red}{-8b})(\color{blue}{10p^3}\color{red}{+8b})=\color{blue}{(10p^3)}^2-\color{red}{(-8b)}^2=100p^{6}-64b^2\)
3. \((10p^3+12b)^2=(10p^3)^2\color{magenta}{+2.(10p^3).(12b)}+(12b)^2=100p^{6}\color{magenta}{+240bp^3}+144b^2\)
4. \((\color{blue}{a}\color{red}{+15})(\color{blue}{a}\color{red}{-15})=\color{blue}{a}^2-\color{red}{15}^2=a^2-225\)
5. \((\color{blue}{q}\color{red}{+7})(\color{blue}{q}\color{red}{-7})=\color{blue}{q}^2-\color{red}{7}^2=q^2-49\)
6. \((-8y+4)^2=(-8y)^2+\color{magenta}{2.(-8y).4}+4^2=64y^2\color{magenta}{-64y}+16\)
7. \((6s^5-4)(6s^5-4)=(6s^5-4)^2=(6s^5)^2\color{magenta}{+2.(6s^5).(-4)}+(-4)^2=36s^{10}\color{magenta}{-48s^5}+16\)
8. \((-16p^4+14q)^2=(-16p^4)^2\color{magenta}{+2.(-16p^4).(14q)}+(14q)^2=256p^{8}\color{magenta}{-448p^4q}+196q^2\)
9. \((12b-8)^2=(12b)^2+\color{magenta}{2.(12b).(-8)}+(-8)^2=144b^2\color{magenta}{-192b}+64\)
10. \((-13a^3-x)^2=(-13a^3)^2\color{magenta}{+2.(-13a^3).(-x)}+(-x)^2=169a^{6}\color{magenta}{+26a^3x}+1x^2\)
11. \((3a-16)^2=(3a)^2+\color{magenta}{2.(3a).(-16)}+(-16)^2=9a^2\color{magenta}{-96a}+256\)
12. \((a+10)^2=a^2+\color{magenta}{2.a.10}+10^2=a^2\color{magenta}{+20a}+100\)