Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

1. \((p+1)(p-1)\)
2. \((4x-5)^2\)
3. \((15b+7)(15b-7)\)
4. \((x-9)^2\)
5. \((10x-13)(-10x-13)\)
6. \((p+4)(p-4)\)
7. \((8x^5-2p)^2\)
8. \((-6p^2+5x)(-6p^2+5x)\)
9. \((15b^5+11)(15b^5-11)\)
10. \((2q-14)(2q-14)\)
11. \((11q^2+15b)(11q^2+15b)\)
12. \((13y^3-14b)(13y^3+14b)\)

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{blue}{p}\color{red}{+1})(\color{blue}{p}\color{red}{-1})=\color{blue}{p}^2-\color{red}{1}^2=p^2-1\)
2. \((4x-5)^2=(4x)^2+\color{magenta}{2.(4x).(-5)}+(-5)^2=16x^2\color{magenta}{-40x}+25\)
3. \((\color{blue}{15b}\color{red}{+7})(\color{blue}{15b}\color{red}{-7})=\color{blue}{(15b)}^2-\color{red}{(7)}^2=225b^2-49\)
4. \((x-9)^2=x^2+\color{magenta}{2.x.(-9)}+(-9)^2=x^2\color{magenta}{-18x}+81\)
5. \((\color{red}{10x}\color{blue}{-13})(\color{red}{-10x}\color{blue}{-13})=\color{blue}{(-13)}^2-\color{red}{(10x)}^2=169-100x^2\)
6. \((\color{blue}{p}\color{red}{+4})(\color{blue}{p}\color{red}{-4})=\color{blue}{p}^2-\color{red}{4}^2=p^2-16\)
7. \((8x^5-2p)^2=(8x^5)^2\color{magenta}{+2.(8x^5).(-2p)}+(-2p)^2=64x^{10}\color{magenta}{-32px^5}+4p^2\)
8. \((-6p^2+5x)(-6p^2+5x)=(-6p^2+5x)^2=(-6p^2)^2\color{magenta}{+2.(-6p^2).(5x)}+(5x)^2=36p^{4}\color{magenta}{-60p^2x}+25x^2\)
9. \((\color{blue}{15b^5}\color{red}{+11})(\color{blue}{15b^5}\color{red}{-11})=\color{blue}{(15b^5)}^2-\color{red}{11}^2=225b^{10}-121\)
10. \((2q-14)(2q-14)=(2q-14)^2=(2q)^2+\color{magenta}{2.(2q).(-14)}+(-14)^2=4q^2\color{magenta}{-56q}+196\)
11. \((11q^2+15b)(11q^2+15b)=(11q^2+15b)^2=(11q^2)^2\color{magenta}{+2.(11q^2).(15b)}+(15b)^2=121q^{4}\color{magenta}{+330bq^2}+225b^2\)
12. \((\color{blue}{13y^3}\color{red}{-14b})(\color{blue}{13y^3}\color{red}{+14b})=\color{blue}{(13y^3)}^2-\color{red}{(-14b)}^2=169y^{6}-196b^2\)