Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{blue}{y}\color{red}{+14})(\color{blue}{y}\color{red}{-14})=\color{blue}{y}^2-\color{red}{14}^2=y^2-196\)
2. \((\color{blue}{-4s}\color{red}{+5})(\color{blue}{-4s}\color{red}{-5})=\color{blue}{(-4s)}^2-\color{red}{(5)}^2=16s^2-25\)
3. \((\color{blue}{5b}\color{red}{-10})(\color{blue}{5b}\color{red}{+10})=\color{blue}{(5b)}^2-\color{red}{(-10)}^2=25b^2-100\)
4. \((-4s+16)(-4s+16)=(-4s+16)^2=(-4s)^2+\color{magenta}{2.(-4s).16}+16^2=16s^2\color{magenta}{-128s}+256\)
5. \((x+5)^2=x^2+\color{magenta}{2.x.5}+5^2=x^2\color{magenta}{+10x}+25\)
6. \((a-6)^2=a^2+\color{magenta}{2.a.(-6)}+(-6)^2=a^2\color{magenta}{-12a}+36\)
7. \((\color{blue}{-7y^3}\color{red}{-3b})(\color{blue}{-7y^3}\color{red}{+3b})=\color{blue}{(-7y^3)}^2-\color{red}{(-3b)}^2=49y^{6}-9b^2\)
8. \((\color{red}{-2b^3}\color{blue}{+8})(\color{red}{2b^3}\color{blue}{+8})=\color{blue}{8}^2-\color{red}{(2b^3)}^2=64-4b^{6}\)
9. \((\color{blue}{-7s^5}\color{red}{+3y})(\color{blue}{-7s^5}\color{red}{-3y})=\color{blue}{(-7s^5)}^2-\color{red}{(3y)}^2=49s^{10}-9y^2\)
10. \((-14x+5)(-14x+5)=(-14x+5)^2=(-14x)^2+\color{magenta}{2.(-14x).5}+5^2=196x^2\color{magenta}{-140x}+25\)
11. \((-3y-9)^2=(-3y)^2+\color{magenta}{2.(-3y).(-9)}+(-9)^2=9y^2\color{magenta}{+54y}+81\)
12. \((\color{blue}{-16x^2}\color{red}{-4s})(\color{blue}{-16x^2}\color{red}{+4s})=\color{blue}{(-16x^2)}^2-\color{red}{(-4s)}^2=256x^{4}-16s^2\)