Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{red}{-x}\color{blue}{-1})(\color{red}{x}\color{blue}{-1})=\color{blue}{(-1)}^2-\color{red}{(x)}^2=1-x^2\)
2. \((\color{blue}{9b^2}\color{red}{-13y})(\color{blue}{9b^2}\color{red}{+13y})=\color{blue}{(9b^2)}^2-\color{red}{(-13y)}^2=81b^{4}-169y^2\)
3. \((-11a^2+5q)(-11a^2+5q)=(-11a^2+5q)^2=(-11a^2)^2\color{magenta}{+2.(-11a^2).(5q)}+(5q)^2=121a^{4}\color{magenta}{-110a^2q}+25q^2\)
4. \((\color{blue}{8y}\color{red}{+3})(\color{blue}{8y}\color{red}{-3})=\color{blue}{(8y)}^2-\color{red}{(3)}^2=64y^2-9\)
5. \((\color{blue}{a}\color{red}{+15})(\color{blue}{a}\color{red}{-15})=\color{blue}{a}^2-\color{red}{15}^2=a^2-225\)
6. \((\color{blue}{7q^3}\color{red}{+8})(\color{blue}{7q^3}\color{red}{-8})=\color{blue}{(7q^3)}^2-\color{red}{8}^2=49q^{6}-64\)
7. \((-15x^4+16b)^2=(-15x^4)^2\color{magenta}{+2.(-15x^4).(16b)}+(16b)^2=225x^{8}\color{magenta}{-480bx^4}+256b^2\)
8. \((\color{red}{10x}\color{blue}{-12})(\color{red}{-10x}\color{blue}{-12})=\color{blue}{(-12)}^2-\color{red}{(10x)}^2=144-100x^2\)
9. \((\color{blue}{16q^3}\color{red}{-11y})(\color{blue}{16q^3}\color{red}{+11y})=\color{blue}{(16q^3)}^2-\color{red}{(-11y)}^2=256q^{6}-121y^2\)
10. \((\color{blue}{a}\color{red}{-11})(\color{blue}{a}\color{red}{+11})=\color{blue}{a}^2-\color{red}{11}^2=a^2-121\)
11. \((12b^4+11)^2=(12b^4)^2\color{magenta}{+2.(12b^4).11}+11^2=144b^{8}\color{magenta}{+264b^4}+121\)
12. \((\color{red}{15p}\color{blue}{+2})(\color{red}{-15p}\color{blue}{+2})=\color{blue}{2}^2-\color{red}{(15p)}^2=4-225p^2\)