Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{blue}{a}\color{red}{+7})(\color{blue}{a}\color{red}{-7})=\color{blue}{a}^2-\color{red}{7}^2=a^2-49\)
2. \((y-3)^2=y^2+\color{magenta}{2.y.(-3)}+(-3)^2=y^2\color{magenta}{-6y}+9\)
3. \((-13q^5+6)(-13q^5+6)=(-13q^5+6)^2=(-13q^5)^2\color{magenta}{+2.(-13q^5).6}+6^2=169q^{10}\color{magenta}{-156q^5}+36\)
4. \((y-8)^2=y^2+\color{magenta}{2.y.(-8)}+(-8)^2=y^2\color{magenta}{-16y}+64\)
5. \((\color{blue}{y}\color{red}{-2})(\color{blue}{y}\color{red}{+2})=\color{blue}{y}^2-\color{red}{2}^2=y^2-4\)
6. \((\color{blue}{p}\color{red}{+15})(\color{blue}{p}\color{red}{-15})=\color{blue}{p}^2-\color{red}{15}^2=p^2-225\)
7. \((-7x^3+8)(-7x^3+8)=(-7x^3+8)^2=(-7x^3)^2\color{magenta}{+2.(-7x^3).8}+8^2=49x^{6}\color{magenta}{-112x^3}+64\)
8. \((6b-1)^2=(6b)^2+\color{magenta}{2.(6b).(-1)}+(-1)^2=36b^2\color{magenta}{-12b}+1\)
9. \((q+9)(q+9)=(q+9)^2=q^2+\color{magenta}{2.q.9}+9^2=q^2\color{magenta}{+18q}+81\)
10. \((\color{red}{-4q^3}\color{blue}{+11})(\color{red}{4q^3}\color{blue}{+11})=\color{blue}{11}^2-\color{red}{(4q^3)}^2=121-16q^{6}\)
11. \((\color{blue}{5x^4}\color{red}{+3})(\color{blue}{5x^4}\color{red}{-3})=\color{blue}{(5x^4)}^2-\color{red}{3}^2=25x^{8}-9\)
12. \((\color{red}{-4s^5}\color{blue}{-12})(\color{red}{4s^5}\color{blue}{-12})=\color{blue}{(-12)}^2-\color{red}{(4s^5)}^2=144-16s^{10}\)