Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{blue}{-2y}\color{red}{+7})(\color{blue}{-2y}\color{red}{-7})=\color{blue}{(-2y)}^2-\color{red}{(7)}^2=4y^2-49\)
2. \((\color{blue}{q}\color{red}{-15})(\color{blue}{q}\color{red}{+15})=\color{blue}{q}^2-\color{red}{15}^2=q^2-225\)
3. \((\color{red}{13q^3}\color{blue}{-14})(\color{red}{-13q^3}\color{blue}{-14})=\color{blue}{(-14)}^2-\color{red}{(13q^3)}^2=196-169q^{6}\)
4. \((\color{blue}{x}\color{red}{-6})(\color{blue}{x}\color{red}{+6})=\color{blue}{x}^2-\color{red}{6}^2=x^2-36\)
5. \((-q+7)(-q+7)=(-q+7)^2=(-q)^2+\color{magenta}{2.(-q).7}+7^2=q^2\color{magenta}{-14q}+49\)
6. \((-3q-1)^2=(-3q)^2+\color{magenta}{2.(-3q).(-1)}+(-1)^2=9q^2\color{magenta}{+6q}+1\)
7. \((14y^3+8a)^2=(14y^3)^2\color{magenta}{+2.(14y^3).(8a)}+(8a)^2=196y^{6}\color{magenta}{+224ay^3}+64a^2\)
8. \((\color{blue}{16y^2}\color{red}{+5b})(\color{blue}{16y^2}\color{red}{-5b})=\color{blue}{(16y^2)}^2-\color{red}{(5b)}^2=256y^{4}-25b^2\)
9. \((-11q+13)^2=(-11q)^2+\color{magenta}{2.(-11q).13}+13^2=121q^2\color{magenta}{-286q}+169\)
10. \((7x^4-12)^2=(7x^4)^2\color{magenta}{+2.(7x^4).(-12)}+(-12)^2=49x^{8}\color{magenta}{-168x^4}+144\)
11. \((-5a^5-16q)^2=(-5a^5)^2\color{magenta}{+2.(-5a^5).(-16q)}+(-16q)^2=25a^{10}\color{magenta}{+160a^5q}+256q^2\)
12. \((\color{blue}{-2p}\color{red}{+3})(\color{blue}{-2p}\color{red}{-3})=\color{blue}{(-2p)}^2-\color{red}{(3)}^2=4p^2-9\)