Odpowiedź:
z.1
( a + b)² = a² + 2a*b + b² ( a - b )² = a² - 2 a*b + b²
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więc
( x + 9 )² = x² + 2 x*9 + 9² = x² + 18 x + 81
( 3 x - 2)² = ( 3 x )² - 2*3 x*2 + 2² = 9 x² - 12 x + 4
( 4 x + 2 y )² = ( 4 x )² + 2*4 x*2 y + ( 2 y)² = 16 x² + 16 x*y + 4 y²
( [tex]\frac{1}{2} x - 5 y )^2 = \frac{1}{4} x^2 - 2*\frac{1}{2} x*5 y + ( 5 y)^2 = \frac{1}{4} x^{2} - 5x*y + 25 y^2[/tex]
( a - b)*(a + b) = a² - b²
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( x - 6)*( x + 6 ) = x² - 6² = x² - 36
( 4 - x )*( 4 + x) = 4² - x² = 16 - x²
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( √2 + 2)² = 2 + 2*√2*2 + 2² = 2 + 4√2 + 4 = 6 + 4√2
( √5 - √3 )² = 5 - 2*√5*√3 + 3 = 8 - 2 [tex]\sqrt{15}[/tex]
( 2 √5 + √2 )² = 4*5 + 2*2√5*√2 + 2 = 22 + 4[tex]\sqrt{10}[/tex]
( √5 + 2)*( √5 - 2) = 5 - 4 = 1
z.2
( 2 x + 1)² - ( 2 x - 1)*( 2 x + 1) = 4 x² + 4 x + 1 - ( 4 x² - 1) = 4 x + 2
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Odpowiedź:
z.1
( a + b)² = a² + 2a*b + b² ( a - b )² = a² - 2 a*b + b²
===================== =======================
więc
( x + 9 )² = x² + 2 x*9 + 9² = x² + 18 x + 81
( 3 x - 2)² = ( 3 x )² - 2*3 x*2 + 2² = 9 x² - 12 x + 4
( 4 x + 2 y )² = ( 4 x )² + 2*4 x*2 y + ( 2 y)² = 16 x² + 16 x*y + 4 y²
( [tex]\frac{1}{2} x - 5 y )^2 = \frac{1}{4} x^2 - 2*\frac{1}{2} x*5 y + ( 5 y)^2 = \frac{1}{4} x^{2} - 5x*y + 25 y^2[/tex]
( a - b)*(a + b) = a² - b²
===================
więc
( x - 6)*( x + 6 ) = x² - 6² = x² - 36
( 4 - x )*( 4 + x) = 4² - x² = 16 - x²
----------------
( √2 + 2)² = 2 + 2*√2*2 + 2² = 2 + 4√2 + 4 = 6 + 4√2
( √5 - √3 )² = 5 - 2*√5*√3 + 3 = 8 - 2 [tex]\sqrt{15}[/tex]
( 2 √5 + √2 )² = 4*5 + 2*2√5*√2 + 2 = 22 + 4[tex]\sqrt{10}[/tex]
( √5 + 2)*( √5 - 2) = 5 - 4 = 1
z.2
( 2 x + 1)² - ( 2 x - 1)*( 2 x + 1) = 4 x² + 4 x + 1 - ( 4 x² - 1) = 4 x + 2
Szczegółowe wyjaśnienie: