Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((b+12)(b+12)=(b+12)^2=b^2+\color{magenta}{2.b.12}+12^2=b^2\color{magenta}{+24b}+144\)
2. \((\color{blue}{9q^3}\color{red}{-16})(\color{blue}{9q^3}\color{red}{+16})=\color{blue}{(9q^3)}^2-\color{red}{(-16)}^2=81q^{6}-256\)
3. \((-15a^4-11)(-15a^4-11)=(-15a^4-11)^2=(-15a^4)^2\color{magenta}{+2.(-15a^4).(-11)}+(-11)^2=225a^{8}\color{magenta}{+330a^4}+121\)
4. \((\color{blue}{14p^5}\color{red}{-6})(\color{blue}{14p^5}\color{red}{+6})=\color{blue}{(14p^5)}^2-\color{red}{(-6)}^2=196p^{10}-36\)
5. \((\color{blue}{x}\color{red}{-2})(\color{blue}{x}\color{red}{+2})=\color{blue}{x}^2-\color{red}{2}^2=x^2-4\)
6. \((\color{red}{-11b^4}\color{blue}{-16})(\color{red}{11b^4}\color{blue}{-16})=\color{blue}{(-16)}^2-\color{red}{(11b^4)}^2=256-121b^{8}\)
7. \((3p^3-5x)(3p^3-5x)=(3p^3-5x)^2=(3p^3)^2\color{magenta}{+2.(3p^3).(-5x)}+(-5x)^2=9p^{6}\color{magenta}{-30p^3x}+25x^2\)
8. \((\color{red}{8y^3}\color{blue}{-11})(\color{red}{-8y^3}\color{blue}{-11})=\color{blue}{(-11)}^2-\color{red}{(8y^3)}^2=121-64y^{6}\)
9. \((\color{blue}{-14x^4}\color{red}{+11})(\color{blue}{-14x^4}\color{red}{-11})=\color{blue}{(-14x^4)}^2-\color{red}{11}^2=196x^{8}-121\)
10. \((a-12)^2=a^2+\color{magenta}{2.a.(-12)}+(-12)^2=a^2\color{magenta}{-24a}+144\)
11. \((\color{blue}{-13s}\color{red}{-6})(\color{blue}{-13s}\color{red}{+6})=\color{blue}{(-13s)}^2-\color{red}{(-6)}^2=169s^2-36\)
12. \((\color{red}{15x^3}\color{blue}{+13b})(\color{red}{-15x^3}\color{blue}{+13b})=\color{blue}{(13b)}^2-\color{red}{(15x^3)}^2=169b^2-225x^{6}\)