Zadanie 1.15-1.
Wykonaj mnożenie. Zredukuj wyrazy podobne.
a) $(x+4)(x+3)$
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\(x^{2}+7x+12\)
b) $(p+6)(p-q)$
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\(p^{2}-pq+6p-6q\)
c) $(p+q)(q-2p)$
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\(-2p^{2}-pq+q^{2}\)
d) $(3x+1)(2x+6)$
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\(6x^{2}+20x+6\)
e) $(a+3b)(3a-2b)$
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\(3a^{2}+7ab-6b^{2}\)
f) $(2a-\tfrac{1}{2}b)(4a-3b)$
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\(8a^{2}-8ab+\tfrac{3}{2}b^{2}\)
g) $(x+3)(x+5)$
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\(x^{2}+8x+15\)
h) $(a+4b)(a-b)$
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\(a^{2}+3ab-4b^{2}\)
i) $(2a+b)(a-1)$
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\(2a^{2}-2a+ab-b\)
j) $(3a-2b)(2b+3)$
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\(6ab+9a-4b^{2}-6b\)
k) $(-2a+b)(6a-2)$
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\(-12a^{2}+6ab+4a-2b\)
l) $(3+4a)(-2b-1)$
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\(-8ab-4a-6b-3\)
m) $(2a+b^2)(a-2b)$
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\(2a^{2}-4ab+ab^{2}-2b^{3}\)
n) $(a^2-3b)(2b-3a)$
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\(-3a^{3}+2a^{2}b+9ab-6b^{2}\)
Zadanie 1.15-2.
Wykonaj mnożenie.
a) $(x-3)(x^2+x-2)$
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\(x^{3}-2x^{2}-5x+6\)
b) $(x-1)(x^2+x-2)$
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\(x^{3}-3x+2\)
c) $(x+3)(2x^2-x+3)$
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\(2x^{3}+5x^{2}+9\)
d) $(x+y-4)(x-y)$
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\(x^{2}-y^{2}-4x+4y\)
e) $(x-y+2)(x+y-3)$
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\(x^{2}-x-y^{2}+5y-6\)
f) $(x^2+x+1)(x^2-x+1)$
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\(x^{4}+x^{2}+1\)
g) $(x+2y+3)(x-2)$
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\(x^{2}+2xy+x-4y-6\)
h) $(2x-y+1)(2x-3)$
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\(4x^{2}-2xy-4x+3y-3\)
i) $(x^2+y)(x+y+2)$
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\(x^{3}+x^{2}y+2x^{2}+xy+y^{2}+2y\)
j) $(x-y)(x^2-2x+1)$
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\(x^{3}-x^{2}y-2x^{2}+2xy+x-y\)
Zadanie 1.15-3.
Uprość wyrażenia.
a) $(a+3)(a-4)+(a-3)(a+4)$
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\(2a^{2}-24\)
b) $(2a-b)(a+3b)-(a-4b)(2a+b)$
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\(b^{2}+12ab\)
c) $3x^2-2x(x+2)-(-x)(2x+y)$
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\(3x^{2}+xy-4x\)
d) $2x^2+3x(x+2)-x(x-3)$
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\(4x^{2}+9x\)
e) $2x(x-2y)(3+y)$
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\(6x^{2}+2x^{2}y-12xy-4xy^{2}\)
f) $-4x(2x-y)(2x+y)$
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\(-16x^{3}+4xy^{2}\)
g) $(3k+5)(4k-2)+2(5-7k)$
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\(12k^{2}\)
h) $(3k-1)(4k-2)-6(1-4k)$
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\(12k^{2}+14k-4\)
i) $(2k-1)(5k+1)-(4k+1)(k-1)$
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\(6k^{2}\)
j) $3k(8k-2)-(6k+1)(4k-1)$
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\(1-4k\)
Zadanie 1.15-4.
Uprość wyrażenie i oblicz jego wartość dla $x=-0{,}5$.
a) $(x+2)(6x+4)-5(x+6)$
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\(6x^{2}+11x-22,\; x=-0{,}5\Rightarrow -26\)
b) $-2(x^4+x^2)+2x^3(x+1)+(x^2-2)(x^2+3)$
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\(x^{4}+2x^{3}-x^{2}-6,\; x=-0{,}5\Rightarrow -\frac{103}{16}\)
Zadanie 1.15-5.
Oblicz.
a) $(\sqrt{3}+2)(\sqrt{3}-1)$
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\(1+\sqrt{3}\)
b) $(\sqrt{3}+\sqrt{2})(2\sqrt{3}-\sqrt{2})$
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\(4+\sqrt{6}\)
c) $(\sqrt{2}+3)(\sqrt{2}-1)$
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\(-1+2\sqrt{2}\)
d) $(\sqrt{5}-2)(\sqrt{5}-3)$
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\(11-5\sqrt{5}\)
e) $(\sqrt{3}-\sqrt{2})(\sqrt{3}-2\sqrt{2})$
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\(7-3\sqrt{6}\)
f) $(2\sqrt{5}+\sqrt{2})(\sqrt{5}+3\sqrt{2})$
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\(16+7\sqrt{10}\)
g) $(\sqrt{3}+\sqrt{2})(\sqrt{3}+\sqrt{2}-1)$
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\(5+2\sqrt{6}-\sqrt{3}-\sqrt{2}\)
h) $(\sqrt{3}+2\sqrt{2})(4\sqrt{3}-8\sqrt{2})$
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\(-20\)
i) $(2\sqrt{5}-4\sqrt{2})(2\sqrt{2}+\sqrt{5})$
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\(-6\)
j) $(2\sqrt{3}-3\sqrt{2})(\sqrt{2}+\sqrt{3})-(4-\sqrt{6})$
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\(-4\)
k) $(\sqrt{5}+2\sqrt{3})(2\sqrt{5}-\sqrt{3})+(6-3\sqrt{15})$
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\(10\)