Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

1. \((-13a^2+11y)^2\)
2. \((6x+1)(6x+1)\)
3. \((s+14)(s+14)\)
4. \((8x-8)(8x-8)\)
5. \((s+14)(s-14)\)
6. \((-6a-4)(6a-4)\)
7. \((10x-5)(-10x-5)\)
8. \((-6x^2-15p)(-6x^2-15p)\)
9. \((9q^3+13)(9q^3+13)\)
10. \((q+11)(q-11)\)
11. \((7a^5-p)(7a^5-p)\)
12. \((-y+3)(-y+3)\)

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((-13a^2+11y)^2=(-13a^2)^2\color{magenta}{+2.(-13a^2).(11y)}+(11y)^2=169a^{4}\color{magenta}{-286a^2y}+121y^2\)
2. \((6x+1)(6x+1)=(6x+1)^2=(6x)^2+\color{magenta}{2.(6x).1}+1^2=36x^2\color{magenta}{+12x}+1\)
3. \((s+14)(s+14)=(s+14)^2=s^2+\color{magenta}{2.s.14}+14^2=s^2\color{magenta}{+28s}+196\)
4. \((8x-8)(8x-8)=(8x-8)^2=(8x)^2+\color{magenta}{2.(8x).(-8)}+(-8)^2=64x^2\color{magenta}{-128x}+64\)
5. \((\color{blue}{s}\color{red}{+14})(\color{blue}{s}\color{red}{-14})=\color{blue}{s}^2-\color{red}{14}^2=s^2-196\)
6. \((\color{red}{-6a}\color{blue}{-4})(\color{red}{6a}\color{blue}{-4})=\color{blue}{(-4)}^2-\color{red}{(6a)}^2=16-36a^2\)
7. \((\color{red}{10x}\color{blue}{-5})(\color{red}{-10x}\color{blue}{-5})=\color{blue}{(-5)}^2-\color{red}{(10x)}^2=25-100x^2\)
8. \((-6x^2-15p)(-6x^2-15p)=(-6x^2-15p)^2=(-6x^2)^2\color{magenta}{+2.(-6x^2).(-15p)}+(-15p)^2=36x^{4}\color{magenta}{+180px^2}+225p^2\)
9. \((9q^3+13)(9q^3+13)=(9q^3+13)^2=(9q^3)^2\color{magenta}{+2.(9q^3).13}+13^2=81q^{6}\color{magenta}{+234q^3}+169\)
10. \((\color{blue}{q}\color{red}{+11})(\color{blue}{q}\color{red}{-11})=\color{blue}{q}^2-\color{red}{11}^2=q^2-121\)
11. \((7a^5-p)(7a^5-p)=(7a^5-p)^2=(7a^5)^2\color{magenta}{+2.(7a^5).(-p)}+(-p)^2=49a^{10}\color{magenta}{-14a^5p}+1p^2\)
12. \((-y+3)(-y+3)=(-y+3)^2=(-y)^2+\color{magenta}{2.(-y).3}+3^2=y^2\color{magenta}{-6y}+9\)