Question

Proszę o pomoc!! Zastosować wzory skróconego mnożenia

Answer 1

[tex]a)\ (4x+5y)^2=(4x)^2+2\cdot4x\cdot5y+(5y)^2=16x^2+40xy+25y^2[/tex]

[tex]b)\ (\sqrt2+b)^2=(\sqrt2)^2+2\cdot\sqrt2\cdot b+b^2=2+2\sqrt2b+b^2[/tex]

[tex]c)\ (3a+\sqrt3)^2=(3a)^2+2\cdot3a\cdot\sqrt3+(\sqrt3)^2=9a^2+6\sqrt3a+3[/tex]

[tex]d)\ (3a-2b)^2=(3a)^2-2\cdot3a\cdot2b+(2b)^2=9a^2-12ab+4b^2[/tex]

[tex]e)\ (2\sqrt2-5x)^2=(2\sqrt2)^2-2\cdot2\sqrt2\cdot5x+(5x)^2=8-20\sqrt2x+25x^2[/tex]

[tex]f)\ (\sqrt2 x-\sqrt8 y)^2=(\sqrt2x)^2-2\cdot\sqrt2x\cdot\sqrt8y+(\sqrt8y)^2=2x^2-8xy+8y^2[/tex]

[tex]d)\ (1-\sqrt5x)(1+\sqrt5x)=1^2-(\sqrt5x)^2=1-5x^2[/tex]

[tex]e)\ (13x+14y)(13x-14y)=(13x)^2-(14y)^2=169x^2-196y^2[/tex]

[tex]f)\ (\sqrt3a-\sqrt6b)(\sqrt3a+\sqrt6b)=(\sqrt3a)^2-(\sqrt6b)^2=3a^2-6b^2[/tex]

Wzory:

[tex](a+b)^2=a^2+2ab+b^2\\\\(a-b)^2=a^2-2ab+b^2\\\\(a-b)(a+b)=a^2-b^2[/tex]