Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{red}{7b^2}\color{blue}{-11y})(\color{red}{-7b^2}\color{blue}{-11y})=\color{blue}{(-11y)}^2-\color{red}{(7b^2)}^2=121y^2-49b^{4}\)
2. \((\color{blue}{9x^4}\color{red}{+4})(\color{blue}{9x^4}\color{red}{-4})=\color{blue}{(9x^4)}^2-\color{red}{4}^2=81x^{8}-16\)
3. \((\color{red}{8x}\color{blue}{+4})(\color{red}{-8x}\color{blue}{+4})=\color{blue}{4}^2-\color{red}{(8x)}^2=16-64x^2\)
4. \((5p^2+2)(5p^2+2)=(5p^2+2)^2=(5p^2)^2\color{magenta}{+2.(5p^2).2}+2^2=25p^{4}\color{magenta}{+20p^2}+4\)
5. \((x+6)^2=x^2+\color{magenta}{2.x.6}+6^2=x^2\color{magenta}{+12x}+36\)
6. \((16x^3-p)(16x^3-p)=(16x^3-p)^2=(16x^3)^2\color{magenta}{+2.(16x^3).(-p)}+(-p)^2=256x^{6}\color{magenta}{-32px^3}+1p^2\)
7. \((\color{red}{9q^5}\color{blue}{-1})(\color{red}{-9q^5}\color{blue}{-1})=\color{blue}{(-1)}^2-\color{red}{(9q^5)}^2=1-81q^{10}\)
8. \((\color{blue}{7y^5}\color{red}{+12p})(\color{blue}{7y^5}\color{red}{-12p})=\color{blue}{(7y^5)}^2-\color{red}{(12p)}^2=49y^{10}-144p^2\)
9. \((\color{blue}{q}\color{red}{+4})(\color{blue}{q}\color{red}{-4})=\color{blue}{q}^2-\color{red}{4}^2=q^2-16\)
10. \((s+11)(s+11)=(s+11)^2=s^2+\color{magenta}{2.s.11}+11^2=s^2\color{magenta}{+22s}+121\)
11. \((6b-14)^2=(6b)^2+\color{magenta}{2.(6b).(-14)}+(-14)^2=36b^2\color{magenta}{-168b}+196\)
12. \((\color{red}{-b^3}\color{blue}{+10a})(\color{red}{b^3}\color{blue}{+10a})=\color{blue}{(10a)}^2-\color{red}{(b^3)}^2=100a^2-b^{6}\)