Question

Simplifique as expressões,

A) (x-5)² - (x-3).(x+3)

B)(4x-2y).(4x+2y)-(3x-4y)²

C)(y-4)²-(2y+5)²+2.(y+2).(y-2)

D)x.(x-5)²+x.(x-2)²

Answer 1

Produtos Notáveis utilizados:

$(a + b)^2 = 2^2 + 2ab + b^2\\(a - b)^2 = 2^2 - 2ab + b^2\\(a + b)(a - b) = a^2 - b^2$

A)

$A=(x-5)^2-(x-3)(x+3)\\A=(x^2-2.x.5+5^2)-(x^2-3^2)\\A=x^2-10x+25-x^2+9\\A=-10x+34\\A=34-10x$

B)

$B=(4x-2y)(4x+2y)-(3x-4y)^2\\B=(4x)^2-(2y)^2-(3x-4y)^2\\B=(4x)^2-(2y)^2-((3x)^2-2\times3x\times4y+(4y)^2)\\B=16x^2-4y^2-(9x^2-24xy+16y^2)\\B=16x^2-4y^2-9x^2+24xy-16y^2\\B=(16x^2-9x^2)+24xy+(-16y^2-4y^2)\\B=7x^2+24xy-20y^2$

C)

$C=(y-4)^2-(2y+5)^2+2(y+2)(y-2)\\C=(y^2-2\timesy\times4+4^2)-((2y)^2+2\times2y\times5+5^2)+2(y^2-2^2)\\C=(y^2-8y+16)-(4y^2+20y+25)+2(y^2-2^2)\\C=y^2-8y+16-4y^2-20y-25+2y^2-8\\C=y^2-4y^2+2y^2-8y-20y+16-25-8\\C=-y^2-28y-17$

D)

$D=x(x-5)^2+x(x-2)^2\\D=x(x^2-2\timesx\times5+5^2)+x(x^2-2\timesx\times2+2^2)\\D=x(x^2-10x+25)+x(x^2-4x+4)\\D=(x^3-10x^2+25x)+(x^3-4x^2+4x)\\D=x^3+x^3-10x^2-4x^2+25x+4x\\D=2x^3-14x^2+29x$