Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((13q^5+8)(13q^5+8)=(13q^5+8)^2=(13q^5)^2\color{magenta}{+2.(13q^5).8}+8^2=169q^{10}\color{magenta}{+208q^5}+64\)
2. \((\color{blue}{q}\color{red}{+1})(\color{blue}{q}\color{red}{-1})=\color{blue}{q}^2-\color{red}{1}^2=q^2-1\)
3. \((y+15)(y+15)=(y+15)^2=y^2+\color{magenta}{2.y.15}+15^2=y^2\color{magenta}{+30y}+225\)
4. \((\color{blue}{s}\color{red}{-4})(\color{blue}{s}\color{red}{+4})=\color{blue}{s}^2-\color{red}{4}^2=s^2-16\)
5. \((15s+7)(15s+7)=(15s+7)^2=(15s)^2+\color{magenta}{2.(15s).7}+7^2=225s^2\color{magenta}{+210s}+49\)
6. \((\color{red}{4s^2}\color{blue}{-11x})(\color{red}{-4s^2}\color{blue}{-11x})=\color{blue}{(-11x)}^2-\color{red}{(4s^2)}^2=121x^2-16s^{4}\)
7. \((\color{blue}{s}\color{red}{-7})(\color{blue}{s}\color{red}{+7})=\color{blue}{s}^2-\color{red}{7}^2=s^2-49\)
8. \((\color{blue}{9x^2}\color{red}{+3p})(\color{blue}{9x^2}\color{red}{-3p})=\color{blue}{(9x^2)}^2-\color{red}{(3p)}^2=81x^{4}-9p^2\)
9. \((-s+11)^2=(-s)^2+\color{magenta}{2.(-s).11}+11^2=s^2\color{magenta}{-22s}+121\)
10. \((b+13)(b+13)=(b+13)^2=b^2+\color{magenta}{2.b.13}+13^2=b^2\color{magenta}{+26b}+169\)
11. \((10s^4+4p)^2=(10s^4)^2\color{magenta}{+2.(10s^4).(4p)}+(4p)^2=100s^{8}\color{magenta}{+80ps^4}+16p^2\)
12. \((\color{red}{9p^2}\color{blue}{+4b})(\color{red}{-9p^2}\color{blue}{+4b})=\color{blue}{(4b)}^2-\color{red}{(9p^2)}^2=16b^2-81p^{4}\)