Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((-9y^3+7x)(-9y^3+7x)=(-9y^3+7x)^2=(-9y^3)^2\color{magenta}{+2.(-9y^3).(7x)}+(7x)^2=81y^{6}\color{magenta}{-126xy^3}+49x^2\)
2. \((\color{blue}{-7p^3}\color{red}{+4x})(\color{blue}{-7p^3}\color{red}{-4x})=\color{blue}{(-7p^3)}^2-\color{red}{(4x)}^2=49p^{6}-16x^2\)
3. \((y-12)^2=y^2+\color{magenta}{2.y.(-12)}+(-12)^2=y^2\color{magenta}{-24y}+144\)
4. \((\color{blue}{y}\color{red}{+5})(\color{blue}{y}\color{red}{-5})=\color{blue}{y}^2-\color{red}{5}^2=y^2-25\)
5. \((\color{red}{-9y}\color{blue}{+12})(\color{red}{9y}\color{blue}{+12})=\color{blue}{12}^2-\color{red}{(9y)}^2=144-81y^2\)
6. \((\color{blue}{a}\color{red}{-12})(\color{blue}{a}\color{red}{+12})=\color{blue}{a}^2-\color{red}{12}^2=a^2-144\)
7. \((-11s^5+12x)^2=(-11s^5)^2\color{magenta}{+2.(-11s^5).(12x)}+(12x)^2=121s^{10}\color{magenta}{-264s^5x}+144x^2\)
8. \((\color{blue}{15s^2}\color{red}{+5})(\color{blue}{15s^2}\color{red}{-5})=\color{blue}{(15s^2)}^2-\color{red}{5}^2=225s^{4}-25\)
9. \((\color{blue}{p}\color{red}{+9})(\color{blue}{p}\color{red}{-9})=\color{blue}{p}^2-\color{red}{9}^2=p^2-81\)
10. \((3y^5-15)^2=(3y^5)^2\color{magenta}{+2.(3y^5).(-15)}+(-15)^2=9y^{10}\color{magenta}{-90y^5}+225\)
11. \((-16a^4-6)(-16a^4-6)=(-16a^4-6)^2=(-16a^4)^2\color{magenta}{+2.(-16a^4).(-6)}+(-6)^2=256a^{8}\color{magenta}{+192a^4}+36\)
12. \((\color{blue}{-x^5}\color{red}{+6s})(\color{blue}{-x^5}\color{red}{-6s})=\color{blue}{(-x^5)}^2-\color{red}{(6s)}^2=x^{10}-36s^2\)