Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{blue}{10q^5}\color{red}{-7})(\color{blue}{10q^5}\color{red}{+7})=\color{blue}{(10q^5)}^2-\color{red}{(-7)}^2=100q^{10}-49\)
2. \((15q^3+16)^2=(15q^3)^2\color{magenta}{+2.(15q^3).16}+16^2=225q^{6}\color{magenta}{+480q^3}+256\)
3. \((5s^5-1)(5s^5-1)=(5s^5-1)^2=(5s^5)^2\color{magenta}{+2.(5s^5).(-1)}+(-1)^2=25s^{10}\color{magenta}{-10s^5}+1\)
4. \((\color{blue}{-p^5}\color{red}{+13})(\color{blue}{-p^5}\color{red}{-13})=\color{blue}{(-p^5)}^2-\color{red}{13}^2=p^{10}-169\)
5. \((\color{red}{10p^2}\color{blue}{+13})(\color{red}{-10p^2}\color{blue}{+13})=\color{blue}{13}^2-\color{red}{(10p^2)}^2=169-100p^{4}\)
6. \((\color{blue}{x}\color{red}{-9})(\color{blue}{x}\color{red}{+9})=\color{blue}{(x)}^2-\color{red}{(-9)}^2=x^2-81\)
7. \((\color{blue}{-7x}\color{red}{+7})(\color{blue}{-7x}\color{red}{-7})=\color{blue}{(-7x)}^2-\color{red}{(7)}^2=49x^2-49\)
8. \((s-10)^2=s^2+\color{magenta}{2.s.(-10)}+(-10)^2=s^2\color{magenta}{-20s}+100\)
9. \((\color{blue}{-8y}\color{red}{-7})(\color{blue}{-8y}\color{red}{+7})=\color{blue}{(-8y)}^2-\color{red}{(-7)}^2=64y^2-49\)
10. \((\color{red}{7q}\color{blue}{-16})(\color{red}{-7q}\color{blue}{-16})=\color{blue}{(-16)}^2-\color{red}{(7q)}^2=256-49q^2\)
11. \((8x^2-5)^2=(8x^2)^2\color{magenta}{+2.(8x^2).(-5)}+(-5)^2=64x^{4}\color{magenta}{-80x^2}+25\)
12. \((b+4)(b+4)=(b+4)^2=b^2+\color{magenta}{2.b.4}+4^2=b^2\color{magenta}{+8b}+16\)