Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((8q-12)^2=(8q)^2+\color{magenta}{2.(8q).(-12)}+(-12)^2=64q^2\color{magenta}{-192q}+144\)
2. \((\color{blue}{7b^2}\color{red}{-14})(\color{blue}{7b^2}\color{red}{+14})=\color{blue}{(7b^2)}^2-\color{red}{(-14)}^2=49b^{4}-196\)
3. \((\color{red}{16s}\color{blue}{+10})(\color{red}{-16s}\color{blue}{+10})=\color{blue}{10}^2-\color{red}{(16s)}^2=100-256s^2\)
4. \((\color{blue}{s}\color{red}{+10})(\color{blue}{s}\color{red}{-10})=\color{blue}{s}^2-\color{red}{10}^2=s^2-100\)
5. \((-8s^5-13)(-8s^5-13)=(-8s^5-13)^2=(-8s^5)^2\color{magenta}{+2.(-8s^5).(-13)}+(-13)^2=64s^{10}\color{magenta}{+208s^5}+169\)
6. \((\color{blue}{-11x^4}\color{red}{-15a})(\color{blue}{-11x^4}\color{red}{+15a})=\color{blue}{(-11x^4)}^2-\color{red}{(-15a)}^2=121x^{8}-225a^2\)
7. \((\color{blue}{4a}\color{red}{+7})(\color{blue}{4a}\color{red}{-7})=\color{blue}{(4a)}^2-\color{red}{(7)}^2=16a^2-49\)
8. \((\color{blue}{12y}\color{red}{+7})(\color{blue}{12y}\color{red}{-7})=\color{blue}{(12y)}^2-\color{red}{(7)}^2=144y^2-49\)
9. \((\color{blue}{y}\color{red}{-1})(\color{blue}{y}\color{red}{+1})=\color{blue}{y}^2-\color{red}{1}^2=y^2-1\)
10. \((12a+5)^2=(12a)^2+\color{magenta}{2.(12a).5}+5^2=144a^2\color{magenta}{+120a}+25\)
11. \((\color{blue}{p}\color{red}{-8})(\color{blue}{p}\color{red}{+8})=\color{blue}{p}^2-\color{red}{8}^2=p^2-64\)
12. \((8q^3+15y)(8q^3+15y)=(8q^3+15y)^2=(8q^3)^2\color{magenta}{+2.(8q^3).(15y)}+(15y)^2=64q^{6}\color{magenta}{+240q^3y}+225y^2\)