Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{blue}{5q^5}\color{red}{+14b})(\color{blue}{5q^5}\color{red}{-14b})=\color{blue}{(5q^5)}^2-\color{red}{(14b)}^2=25q^{10}-196b^2\)
2. \((a+3)^2=a^2+\color{magenta}{2.a.3}+3^2=a^2\color{magenta}{+6a}+9\)
3. \((-10p^4-5)(-10p^4-5)=(-10p^4-5)^2=(-10p^4)^2\color{magenta}{+2.(-10p^4).(-5)}+(-5)^2=100p^{8}\color{magenta}{+100p^4}+25\)
4. \((\color{blue}{-15x}\color{red}{+15})(\color{blue}{-15x}\color{red}{-15})=\color{blue}{(-15x)}^2-\color{red}{(15)}^2=225x^2-225\)
5. \((16q^2+4b)(16q^2+4b)=(16q^2+4b)^2=(16q^2)^2\color{magenta}{+2.(16q^2).(4b)}+(4b)^2=256q^{4}\color{magenta}{+128bq^2}+16b^2\)
6. \((\color{blue}{2b^3}\color{red}{+10})(\color{blue}{2b^3}\color{red}{-10})=\color{blue}{(2b^3)}^2-\color{red}{10}^2=4b^{6}-100\)
7. \((s-11)^2=s^2+\color{magenta}{2.s.(-11)}+(-11)^2=s^2\color{magenta}{-22s}+121\)
8. \((x+2)^2=x^2+\color{magenta}{2.x.2}+2^2=x^2\color{magenta}{+4x}+4\)
9. \((\color{blue}{-16q^4}\color{red}{+15})(\color{blue}{-16q^4}\color{red}{-15})=\color{blue}{(-16q^4)}^2-\color{red}{15}^2=256q^{8}-225\)
10. \((\color{blue}{-14p}\color{red}{+10})(\color{blue}{-14p}\color{red}{-10})=\color{blue}{(-14p)}^2-\color{red}{(10)}^2=196p^2-100\)
11. \((\color{red}{3x^4}\color{blue}{-10})(\color{red}{-3x^4}\color{blue}{-10})=\color{blue}{(-10)}^2-\color{red}{(3x^4)}^2=100-9x^{8}\)
12. \((-7s+3)^2=(-7s)^2+\color{magenta}{2.(-7s).3}+3^2=49s^2\color{magenta}{-42s}+9\)