Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{red}{-15q^5}\color{blue}{+16})(\color{red}{15q^5}\color{blue}{+16})=\color{blue}{16}^2-\color{red}{(15q^5)}^2=256-225q^{10}\)
2. \((\color{blue}{b}\color{red}{+9})(\color{blue}{b}\color{red}{-9})=\color{blue}{b}^2-\color{red}{9}^2=b^2-81\)
3. \((\color{blue}{-13b^2}\color{red}{-3})(\color{blue}{-13b^2}\color{red}{+3})=\color{blue}{(-13b^2)}^2-\color{red}{(-3)}^2=169b^{4}-9\)
4. \((\color{blue}{-3x^4}\color{red}{-16})(\color{blue}{-3x^4}\color{red}{+16})=\color{blue}{(-3x^4)}^2-\color{red}{(-16)}^2=9x^{8}-256\)
5. \((-9y-8)(-9y-8)=(-9y-8)^2=(-9y)^2+\color{magenta}{2.(-9y).(-8)}+(-8)^2=81y^2\color{magenta}{+144y}+64\)
6. \((\color{blue}{-7q}\color{red}{-16})(\color{blue}{-7q}\color{red}{+16})=\color{blue}{(-7q)}^2-\color{red}{(-16)}^2=49q^2-256\)
7. \((\color{red}{7s^2}\color{blue}{+12})(\color{red}{-7s^2}\color{blue}{+12})=\color{blue}{12}^2-\color{red}{(7s^2)}^2=144-49s^{4}\)
8. \((\color{blue}{-5y}\color{red}{+11})(\color{blue}{-5y}\color{red}{-11})=\color{blue}{(-5y)}^2-\color{red}{(11)}^2=25y^2-121\)
9. \((\color{blue}{-16p^4}\color{red}{-3})(\color{blue}{-16p^4}\color{red}{+3})=\color{blue}{(-16p^4)}^2-\color{red}{(-3)}^2=256p^{8}-9\)
10. \((x+9)(x+9)=(x+9)^2=x^2+\color{magenta}{2.x.9}+9^2=x^2\color{magenta}{+18x}+81\)
11. \((\color{blue}{p}\color{red}{-7})(\color{blue}{p}\color{red}{+7})=\color{blue}{p}^2-\color{red}{7}^2=p^2-49\)
12. \((-4x+2)(-4x+2)=(-4x+2)^2=(-4x)^2+\color{magenta}{2.(-4x).2}+2^2=16x^2\color{magenta}{-16x}+4\)