Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{blue}{s}\color{red}{-6})(\color{blue}{s}\color{red}{+6})=\color{blue}{s}^2-\color{red}{6}^2=s^2-36\)
2. \((\color{blue}{q}\color{red}{-1})(\color{blue}{q}\color{red}{+1})=\color{blue}{q}^2-\color{red}{1}^2=q^2-1\)
3. \((\color{blue}{9b^2}\color{red}{-15})(\color{blue}{9b^2}\color{red}{+15})=\color{blue}{(9b^2)}^2-\color{red}{(-15)}^2=81b^{4}-225\)
4. \((7y-2)^2=(7y)^2+\color{magenta}{2.(7y).(-2)}+(-2)^2=49y^2\color{magenta}{-28y}+4\)
5. \((2q^2+13)(2q^2+13)=(2q^2+13)^2=(2q^2)^2\color{magenta}{+2.(2q^2).13}+13^2=4q^{4}\color{magenta}{+52q^2}+169\)
6. \((-10a^4+9)(-10a^4+9)=(-10a^4+9)^2=(-10a^4)^2\color{magenta}{+2.(-10a^4).9}+9^2=100a^{8}\color{magenta}{-180a^4}+81\)
7. \((\color{red}{y}\color{blue}{-8})(\color{red}{-y}\color{blue}{-8})=\color{blue}{(-8)}^2-\color{red}{(y)}^2=64-y^2\)
8. \((\color{blue}{x}\color{red}{+10})(\color{blue}{x}\color{red}{-10})=\color{blue}{x}^2-\color{red}{10}^2=x^2-100\)
9. \((\color{red}{5q^4}\color{blue}{+3})(\color{red}{-5q^4}\color{blue}{+3})=\color{blue}{3}^2-\color{red}{(5q^4)}^2=9-25q^{8}\)
10. \((15p^5+12)^2=(15p^5)^2\color{magenta}{+2.(15p^5).12}+12^2=225p^{10}\color{magenta}{+360p^5}+144\)
11. \((\color{red}{12x}\color{blue}{+4})(\color{red}{-12x}\color{blue}{+4})=\color{blue}{4}^2-\color{red}{(12x)}^2=16-144x^2\)
12. \((15a^3+4)(15a^3+4)=(15a^3+4)^2=(15a^3)^2\color{magenta}{+2.(15a^3).4}+4^2=225a^{6}\color{magenta}{+120a^3}+16\)