Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{red}{-14q^3}\color{blue}{+16})(\color{red}{14q^3}\color{blue}{+16})=\color{blue}{16}^2-\color{red}{(14q^3)}^2=256-196q^{6}\)
2. \((7b+2)(7b+2)=(7b+2)^2=(7b)^2+\color{magenta}{2.(7b).2}+2^2=49b^2\color{magenta}{+28b}+4\)
3. \((\color{blue}{a}\color{red}{+11})(\color{blue}{a}\color{red}{-11})=\color{blue}{a}^2-\color{red}{11}^2=a^2-121\)
4. \((\color{red}{6a}\color{blue}{-8})(\color{red}{-6a}\color{blue}{-8})=\color{blue}{(-8)}^2-\color{red}{(6a)}^2=64-36a^2\)
5. \((\color{red}{-7s^4}\color{blue}{+2a})(\color{red}{7s^4}\color{blue}{+2a})=\color{blue}{(2a)}^2-\color{red}{(7s^4)}^2=4a^2-49s^{8}\)
6. \((\color{red}{-16x^4}\color{blue}{+6q})(\color{red}{16x^4}\color{blue}{+6q})=\color{blue}{(6q)}^2-\color{red}{(16x^4)}^2=36q^2-256x^{8}\)
7. \((b+5)(b+5)=(b+5)^2=b^2+\color{magenta}{2.b.5}+5^2=b^2\color{magenta}{+10b}+25\)
8. \((\color{red}{-16a^4}\color{blue}{-6})(\color{red}{16a^4}\color{blue}{-6})=\color{blue}{(-6)}^2-\color{red}{(16a^4)}^2=36-256a^{8}\)
9. \((-12q^3-2y)^2=(-12q^3)^2\color{magenta}{+2.(-12q^3).(-2y)}+(-2y)^2=144q^{6}\color{magenta}{+48q^3y}+4y^2\)
10. \((s-11)^2=s^2+\color{magenta}{2.s.(-11)}+(-11)^2=s^2\color{magenta}{-22s}+121\)
11. \((\color{red}{8s^2}\color{blue}{+p})(\color{red}{-8s^2}\color{blue}{+p})=\color{blue}{(1p)}^2-\color{red}{(8s^2)}^2=1p^2-64s^{4}\)
12. \((-a^3-6b)(-a^3-6b)=(-a^3-6b)^2=(-a^3)^2\color{magenta}{+2.(-a^3).(-6b)}+(-6b)^2=a^{6}\color{magenta}{+12a^3b}+36b^2\)