Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((15q+9)(15q+9)=(15q+9)^2=(15q)^2+\color{magenta}{2.(15q).9}+9^2=225q^2\color{magenta}{+270q}+81\)
2. \((\color{blue}{-p^2}\color{red}{-2a})(\color{blue}{-p^2}\color{red}{+2a})=\color{blue}{(-p^2)}^2-\color{red}{(-2a)}^2=p^{4}-4a^2\)
3. \((q+11)(q+11)=(q+11)^2=q^2+\color{magenta}{2.q.11}+11^2=q^2\color{magenta}{+22q}+121\)
4. \((\color{red}{-11x^4}\color{blue}{+10})(\color{red}{11x^4}\color{blue}{+10})=\color{blue}{10}^2-\color{red}{(11x^4)}^2=100-121x^{8}\)
5. \((-9a^5+3x)(-9a^5+3x)=(-9a^5+3x)^2=(-9a^5)^2\color{magenta}{+2.(-9a^5).(3x)}+(3x)^2=81a^{10}\color{magenta}{-54a^5x}+9x^2\)
6. \((\color{red}{-8a^3}\color{blue}{+12x})(\color{red}{8a^3}\color{blue}{+12x})=\color{blue}{(12x)}^2-\color{red}{(8a^3)}^2=144x^2-64a^{6}\)
7. \((\color{red}{6s^3}\color{blue}{-3})(\color{red}{-6s^3}\color{blue}{-3})=\color{blue}{(-3)}^2-\color{red}{(6s^3)}^2=9-36s^{6}\)
8. \((\color{blue}{q}\color{red}{+15})(\color{blue}{q}\color{red}{-15})=\color{blue}{q}^2-\color{red}{15}^2=q^2-225\)
9. \((15b^5-2)^2=(15b^5)^2\color{magenta}{+2.(15b^5).(-2)}+(-2)^2=225b^{10}\color{magenta}{-60b^5}+4\)
10. \((-p^4-4)(-p^4-4)=(-p^4-4)^2=(-p^4)^2\color{magenta}{+2.(-p^4).(-4)}+(-4)^2=1p^{8}\color{magenta}{+8p^4}+16\)
11. \((-14a^2-15)^2=(-14a^2)^2\color{magenta}{+2.(-14a^2).(-15)}+(-15)^2=196a^{4}\color{magenta}{+420a^2}+225\)
12. \((6a+7)^2=(6a)^2+\color{magenta}{2.(6a).7}+7^2=36a^2\color{magenta}{+84a}+49\)