Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((-5p+7)(-5p+7)=(-5p+7)^2=(-5p)^2+\color{magenta}{2.(-5p).7}+7^2=25p^2\color{magenta}{-70p}+49\)
2. \((\color{blue}{-13a}\color{red}{-10})(\color{blue}{-13a}\color{red}{+10})=\color{blue}{(-13a)}^2-\color{red}{(-10)}^2=169a^2-100\)
3. \((-14q^3-7b)(-14q^3-7b)=(-14q^3-7b)^2=(-14q^3)^2\color{magenta}{+2.(-14q^3).(-7b)}+(-7b)^2=196q^{6}\color{magenta}{+196bq^3}+49b^2\)
4. \((16x^4+6)^2=(16x^4)^2\color{magenta}{+2.(16x^4).6}+6^2=256x^{8}\color{magenta}{+192x^4}+36\)
5. \((x+4)^2=x^2+\color{magenta}{2.x.4}+4^2=x^2\color{magenta}{+8x}+16\)
6. \((\color{red}{-7q^2}\color{blue}{+14})(\color{red}{7q^2}\color{blue}{+14})=\color{blue}{14}^2-\color{red}{(7q^2)}^2=196-49q^{4}\)
7. \((\color{red}{-11x^4}\color{blue}{+4})(\color{red}{11x^4}\color{blue}{+4})=\color{blue}{4}^2-\color{red}{(11x^4)}^2=16-121x^{8}\)
8. \((\color{blue}{9q}\color{red}{+10})(\color{blue}{9q}\color{red}{-10})=\color{blue}{(9q)}^2-\color{red}{(10)}^2=81q^2-100\)
9. \((4x^4-8)(4x^4-8)=(4x^4-8)^2=(4x^4)^2\color{magenta}{+2.(4x^4).(-8)}+(-8)^2=16x^{8}\color{magenta}{-64x^4}+64\)
10. \((\color{red}{-13a^2}\color{blue}{-5})(\color{red}{13a^2}\color{blue}{-5})=\color{blue}{(-5)}^2-\color{red}{(13a^2)}^2=25-169a^{4}\)
11. \((-9a^2+11x)^2=(-9a^2)^2\color{magenta}{+2.(-9a^2).(11x)}+(11x)^2=81a^{4}\color{magenta}{-198a^2x}+121x^2\)
12. \((\color{blue}{p}\color{red}{+11})(\color{blue}{p}\color{red}{-11})=\color{blue}{p}^2-\color{red}{11}^2=p^2-121\)