Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((q+6)^2=q^2+\color{magenta}{2.q.6}+6^2=q^2\color{magenta}{+12q}+36\)
2. \((-15x^5+16a)(-15x^5+16a)=(-15x^5+16a)^2=(-15x^5)^2\color{magenta}{+2.(-15x^5).(16a)}+(16a)^2=225x^{10}\color{magenta}{-480ax^5}+256a^2\)
3. \((\color{blue}{-14s}\color{red}{-9})(\color{blue}{-14s}\color{red}{+9})=\color{blue}{(-14s)}^2-\color{red}{(-9)}^2=196s^2-81\)
4. \((\color{blue}{a}\color{red}{-6})(\color{blue}{a}\color{red}{+6})=\color{blue}{a}^2-\color{red}{6}^2=a^2-36\)
5. \((\color{blue}{y}\color{red}{+8})(\color{blue}{y}\color{red}{-8})=\color{blue}{y}^2-\color{red}{8}^2=y^2-64\)
6. \((\color{red}{15a^3}\color{blue}{-16})(\color{red}{-15a^3}\color{blue}{-16})=\color{blue}{(-16)}^2-\color{red}{(15a^3)}^2=256-225a^{6}\)
7. \((x+11)^2=x^2+\color{magenta}{2.x.11}+11^2=x^2\color{magenta}{+22x}+121\)
8. \((-15b+16)^2=(-15b)^2+\color{magenta}{2.(-15b).16}+16^2=225b^2\color{magenta}{-480b}+256\)
9. \((b-15)(b-15)=(b-15)^2=b^2+\color{magenta}{2.b.(-15)}+(-15)^2=b^2\color{magenta}{-30b}+225\)
10. \((\color{red}{-5s^2}\color{blue}{+14})(\color{red}{5s^2}\color{blue}{+14})=\color{blue}{14}^2-\color{red}{(5s^2)}^2=196-25s^{4}\)
11. \((\color{blue}{x}\color{red}{+7})(\color{blue}{x}\color{red}{-7})=\color{blue}{x}^2-\color{red}{7}^2=x^2-49\)
12. \((\color{blue}{b}\color{red}{-3})(\color{blue}{b}\color{red}{+3})=\color{blue}{b}^2-\color{red}{3}^2=b^2-9\)