Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{red}{6s^5}\color{blue}{-10a})(\color{red}{-6s^5}\color{blue}{-10a})=\color{blue}{(-10a)}^2-\color{red}{(6s^5)}^2=100a^2-36s^{10}\)
2. \((\color{blue}{7s^5}\color{red}{-9})(\color{blue}{7s^5}\color{red}{+9})=\color{blue}{(7s^5)}^2-\color{red}{(-9)}^2=49s^{10}-81\)
3. \((\color{blue}{4p}\color{red}{+9})(\color{blue}{4p}\color{red}{-9})=\color{blue}{(4p)}^2-\color{red}{(9)}^2=16p^2-81\)
4. \((9x^5-12)^2=(9x^5)^2\color{magenta}{+2.(9x^5).(-12)}+(-12)^2=81x^{10}\color{magenta}{-216x^5}+144\)
5. \((p+5)^2=p^2+\color{magenta}{2.p.5}+5^2=p^2\color{magenta}{+10p}+25\)
6. \((7y-4)^2=(7y)^2+\color{magenta}{2.(7y).(-4)}+(-4)^2=49y^2\color{magenta}{-56y}+16\)
7. \((-9p-11)^2=(-9p)^2+\color{magenta}{2.(-9p).(-11)}+(-11)^2=81p^2\color{magenta}{+198p}+121\)
8. \((8q^3-3)^2=(8q^3)^2\color{magenta}{+2.(8q^3).(-3)}+(-3)^2=64q^{6}\color{magenta}{-48q^3}+9\)
9. \((\color{blue}{a}\color{red}{+7})(\color{blue}{a}\color{red}{-7})=\color{blue}{a}^2-\color{red}{7}^2=a^2-49\)
10. \((\color{blue}{-13s^4}\color{red}{-8})(\color{blue}{-13s^4}\color{red}{+8})=\color{blue}{(-13s^4)}^2-\color{red}{(-8)}^2=169s^{8}-64\)
11. \((\color{blue}{s}\color{red}{+9})(\color{blue}{s}\color{red}{-9})=\color{blue}{s}^2-\color{red}{9}^2=s^2-81\)
12. \((s+14)(s+14)=(s+14)^2=s^2+\color{magenta}{2.s.14}+14^2=s^2\color{magenta}{+28s}+196\)