Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{blue}{7s^5}\color{red}{-8a})(\color{blue}{7s^5}\color{red}{+8a})=\color{blue}{(7s^5)}^2-\color{red}{(-8a)}^2=49s^{10}-64a^2\)
2. \((\color{blue}{-10b^4}\color{red}{+14})(\color{blue}{-10b^4}\color{red}{-14})=\color{blue}{(-10b^4)}^2-\color{red}{14}^2=100b^{8}-196\)
3. \((\color{red}{3p}\color{blue}{-11})(\color{red}{-3p}\color{blue}{-11})=\color{blue}{(-11)}^2-\color{red}{(3p)}^2=121-9p^2\)
4. \((5q^4-16x)^2=(5q^4)^2\color{magenta}{+2.(5q^4).(-16x)}+(-16x)^2=25q^{8}\color{magenta}{-160q^4x}+256x^2\)
5. \((\color{blue}{10p}\color{red}{+11})(\color{blue}{10p}\color{red}{-11})=\color{blue}{(10p)}^2-\color{red}{(11)}^2=100p^2-121\)
6. \((\color{blue}{-5p^5}\color{red}{-14a})(\color{blue}{-5p^5}\color{red}{+14a})=\color{blue}{(-5p^5)}^2-\color{red}{(-14a)}^2=25p^{10}-196a^2\)
7. \((5s^2-15)(5s^2-15)=(5s^2-15)^2=(5s^2)^2\color{magenta}{+2.(5s^2).(-15)}+(-15)^2=25s^{4}\color{magenta}{-150s^2}+225\)
8. \((\color{blue}{3b}\color{red}{+15})(\color{blue}{3b}\color{red}{-15})=\color{blue}{(3b)}^2-\color{red}{(15)}^2=9b^2-225\)
9. \((\color{blue}{5y^3}\color{red}{-3})(\color{blue}{5y^3}\color{red}{+3})=\color{blue}{(5y^3)}^2-\color{red}{(-3)}^2=25y^{6}-9\)
10. \((-2q+5)(-2q+5)=(-2q+5)^2=(-2q)^2+\color{magenta}{2.(-2q).5}+5^2=4q^2\color{magenta}{-20q}+25\)
11. \((\color{red}{2y}\color{blue}{+13})(\color{red}{-2y}\color{blue}{+13})=\color{blue}{13}^2-\color{red}{(2y)}^2=169-4y^2\)
12. \((y+11)^2=y^2+\color{magenta}{2.y.11}+11^2=y^2\color{magenta}{+22y}+121\)