Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

1. \((q+11)(q-11)\)
2. \((a-2)^2\)
3. \((6p^5-13)^2\)
4. \((-14x^2+16)^2\)
5. \((b+6)(b+6)\)
6. \((2y^5-11)(2y^5+11)\)
7. \((-y-11)(-y+11)\)
8. \((x-11)(x+11)\)
9. \((-s^3+16x)(-s^3+16x)\)
10. \((-14p^5-s)(-14p^5-s)\)
11. \((-8x^2+1)(-8x^2+1)\)
12. \((a+14)(a-14)\)

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{blue}{q}\color{red}{+11})(\color{blue}{q}\color{red}{-11})=\color{blue}{q}^2-\color{red}{11}^2=q^2-121\)
2. \((a-2)^2=a^2+\color{magenta}{2.a.(-2)}+(-2)^2=a^2\color{magenta}{-4a}+4\)
3. \((6p^5-13)^2=(6p^5)^2\color{magenta}{+2.(6p^5).(-13)}+(-13)^2=36p^{10}\color{magenta}{-156p^5}+169\)
4. \((-14x^2+16)^2=(-14x^2)^2\color{magenta}{+2.(-14x^2).16}+16^2=196x^{4}\color{magenta}{-448x^2}+256\)
5. \((b+6)(b+6)=(b+6)^2=b^2+\color{magenta}{2.b.6}+6^2=b^2\color{magenta}{+12b}+36\)
6. \((\color{blue}{2y^5}\color{red}{-11})(\color{blue}{2y^5}\color{red}{+11})=\color{blue}{(2y^5)}^2-\color{red}{(-11)}^2=4y^{10}-121\)
7. \((\color{blue}{-y}\color{red}{-11})(\color{blue}{-y}\color{red}{+11})=\color{blue}{(-y)}^2-\color{red}{(-11)}^2=y^2-121\)
8. \((\color{blue}{x}\color{red}{-11})(\color{blue}{x}\color{red}{+11})=\color{blue}{x}^2-\color{red}{11}^2=x^2-121\)
9. \((-s^3+16x)(-s^3+16x)=(-s^3+16x)^2=(-s^3)^2\color{magenta}{+2.(-s^3).(16x)}+(16x)^2=s^{6}\color{magenta}{-32s^3x}+256x^2\)
10. \((-14p^5-s)(-14p^5-s)=(-14p^5-s)^2=(-14p^5)^2\color{magenta}{+2.(-14p^5).(-s)}+(-s)^2=196p^{10}\color{magenta}{+28p^5s}+1s^2\)
11. \((-8x^2+1)(-8x^2+1)=(-8x^2+1)^2=(-8x^2)^2\color{magenta}{+2.(-8x^2).1}+1^2=64x^{4}\color{magenta}{-16x^2}+1\)
12. \((\color{blue}{a}\color{red}{+14})(\color{blue}{a}\color{red}{-14})=\color{blue}{a}^2-\color{red}{14}^2=a^2-196\)