Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{blue}{-15p^2}\color{red}{+10})(\color{blue}{-15p^2}\color{red}{-10})=\color{blue}{(-15p^2)}^2-\color{red}{10}^2=225p^{4}-100\)
2. \((\color{red}{14p^5}\color{blue}{+7})(\color{red}{-14p^5}\color{blue}{+7})=\color{blue}{7}^2-\color{red}{(14p^5)}^2=49-196p^{10}\)
3. \((-4s^5+3)^2=(-4s^5)^2\color{magenta}{+2.(-4s^5).3}+3^2=16s^{10}\color{magenta}{-24s^5}+9\)
4. \((\color{blue}{y}\color{red}{-11})(\color{blue}{y}\color{red}{+11})=\color{blue}{(y)}^2-\color{red}{(-11)}^2=y^2-121\)
5. \((4b-2)(4b-2)=(4b-2)^2=(4b)^2+\color{magenta}{2.(4b).(-2)}+(-2)^2=16b^2\color{magenta}{-16b}+4\)
6. \((16p+7)(16p+7)=(16p+7)^2=(16p)^2+\color{magenta}{2.(16p).7}+7^2=256p^2\color{magenta}{+224p}+49\)
7. \((9q-12)(9q-12)=(9q-12)^2=(9q)^2+\color{magenta}{2.(9q).(-12)}+(-12)^2=81q^2\color{magenta}{-216q}+144\)
8. \((\color{blue}{-5y^5}\color{red}{-16})(\color{blue}{-5y^5}\color{red}{+16})=\color{blue}{(-5y^5)}^2-\color{red}{(-16)}^2=25y^{10}-256\)
9. \((\color{red}{12q}\color{blue}{-14})(\color{red}{-12q}\color{blue}{-14})=\color{blue}{(-14)}^2-\color{red}{(12q)}^2=196-144q^2\)
10. \((x+3)(x+3)=(x+3)^2=x^2+\color{magenta}{2.x.3}+3^2=x^2\color{magenta}{+6x}+9\)
11. \((\color{blue}{-2x^5}\color{red}{-14})(\color{blue}{-2x^5}\color{red}{+14})=\color{blue}{(-2x^5)}^2-\color{red}{(-14)}^2=4x^{10}-196\)
12. \((-12a^5+8)^2=(-12a^5)^2\color{magenta}{+2.(-12a^5).8}+8^2=144a^{10}\color{magenta}{-192a^5}+64\)