Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((a+7)^2=a^2+\color{magenta}{2.a.7}+7^2=a^2\color{magenta}{+14a}+49\)
2. \((\color{blue}{a}\color{red}{+5})(\color{blue}{a}\color{red}{-5})=\color{blue}{a}^2-\color{red}{5}^2=a^2-25\)
3. \((-16x^2-15b)(-16x^2-15b)=(-16x^2-15b)^2=(-16x^2)^2\color{magenta}{+2.(-16x^2).(-15b)}+(-15b)^2=256x^{4}\color{magenta}{+480bx^2}+225b^2\)
4. \((\color{blue}{-4q}\color{red}{+14})(\color{blue}{-4q}\color{red}{-14})=\color{blue}{(-4q)}^2-\color{red}{(14)}^2=16q^2-196\)
5. \((\color{blue}{p}\color{red}{+1})(\color{blue}{p}\color{red}{-1})=\color{blue}{p}^2-\color{red}{1}^2=p^2-1\)
6. \((\color{blue}{4s}\color{red}{-5})(\color{blue}{4s}\color{red}{+5})=\color{blue}{(4s)}^2-\color{red}{(-5)}^2=16s^2-25\)
7. \((\color{red}{b^5}\color{blue}{-5})(\color{red}{-b^5}\color{blue}{-5})=\color{blue}{(-5)}^2-\color{red}{(b^5)}^2=25-b^{10}\)
8. \((\color{blue}{p}\color{red}{-4})(\color{blue}{p}\color{red}{+4})=\color{blue}{p}^2-\color{red}{4}^2=p^2-16\)
9. \((-q^2-2)(-q^2-2)=(-q^2-2)^2=(-q^2)^2\color{magenta}{+2.(-q^2).(-2)}+(-2)^2=1q^{4}\color{magenta}{+4q^2}+4\)
10. \((-2y+5)^2=(-2y)^2+\color{magenta}{2.(-2y).5}+5^2=4y^2\color{magenta}{-20y}+25\)
11. \((\color{blue}{-2b}\color{red}{-16})(\color{blue}{-2b}\color{red}{+16})=\color{blue}{(-2b)}^2-\color{red}{(-16)}^2=4b^2-256\)
12. \((\color{blue}{6y}\color{red}{-15})(\color{blue}{6y}\color{red}{+15})=\color{blue}{(6y)}^2-\color{red}{(-15)}^2=36y^2-225\)