Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

1. \((3a^3+6)^2\)
2. \((5x^5-12)(5x^5-12)\)
3. \((-11y-13)(-11y-13)\)
4. \((12y^2-16)(-12y^2-16)\)
5. \((-10p-8)(-10p-8)\)
6. \((p+15)(p-15)\)
7. \((5p^2+14b)(-5p^2+14b)\)
8. \((-q+4)(q+4)\)
9. \((q-4)(q-4)\)
10. \((-14q-5)(14q-5)\)
11. \((7q-6)(-7q-6)\)
12. \((8p+16)(-8p+16)\)

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((3a^3+6)^2=(3a^3)^2\color{magenta}{+2.(3a^3).6}+6^2=9a^{6}\color{magenta}{+36a^3}+36\)
2. \((5x^5-12)(5x^5-12)=(5x^5-12)^2=(5x^5)^2\color{magenta}{+2.(5x^5).(-12)}+(-12)^2=25x^{10}\color{magenta}{-120x^5}+144\)
3. \((-11y-13)(-11y-13)=(-11y-13)^2=(-11y)^2+\color{magenta}{2.(-11y).(-13)}+(-13)^2=121y^2\color{magenta}{+286y}+169\)
4. \((\color{red}{12y^2}\color{blue}{-16})(\color{red}{-12y^2}\color{blue}{-16})=\color{blue}{(-16)}^2-\color{red}{(12y^2)}^2=256-144y^{4}\)
5. \((-10p-8)(-10p-8)=(-10p-8)^2=(-10p)^2+\color{magenta}{2.(-10p).(-8)}+(-8)^2=100p^2\color{magenta}{+160p}+64\)
6. \((\color{blue}{p}\color{red}{+15})(\color{blue}{p}\color{red}{-15})=\color{blue}{p}^2-\color{red}{15}^2=p^2-225\)
7. \((\color{red}{5p^2}\color{blue}{+14b})(\color{red}{-5p^2}\color{blue}{+14b})=\color{blue}{(14b)}^2-\color{red}{(5p^2)}^2=196b^2-25p^{4}\)
8. \((\color{red}{-q}\color{blue}{+4})(\color{red}{q}\color{blue}{+4})=\color{blue}{4}^2-\color{red}{(q)}^2=16-q^2\)
9. \((q-4)(q-4)=(q-4)^2=q^2+\color{magenta}{2.q.(-4)}+(-4)^2=q^2\color{magenta}{-8q}+16\)
10. \((\color{red}{-14q}\color{blue}{-5})(\color{red}{14q}\color{blue}{-5})=\color{blue}{(-5)}^2-\color{red}{(14q)}^2=25-196q^2\)
11. \((\color{red}{7q}\color{blue}{-6})(\color{red}{-7q}\color{blue}{-6})=\color{blue}{(-6)}^2-\color{red}{(7q)}^2=36-49q^2\)
12. \((\color{red}{8p}\color{blue}{+16})(\color{red}{-8p}\color{blue}{+16})=\color{blue}{16}^2-\color{red}{(8p)}^2=256-64p^2\)