Question

3) determine a forma reduzida dos produtos a) (x² +2) .(3x³+ 10x-1) b) (x+3)² .(x³ - 4x+4) c) (x-y+5) . 2x-5y - 11)​

Answer 1

Explicação passo-a-passo:

$a) \left(x^2+2\right)\left(3x^3+10x-1\right)\\=x^2\cdot \:3x^3+x^2\cdot \:10x+x^2\left(-1\right)+2\cdot \:3x^3+2\cdot \:10x+2\left(-1\right)\\=3x^3x^2+10x^2x-1\cdot \:x^2+2\cdot \:3x^3+2\cdot \:10x-2\cdot \:1\\=3x^5+16x^3-x^2+20x-2$

$b) \left(x+3\right)^2\left(x^3-4x+4\right)\\=\left(x+3\right)^2x^3+\left(x+3\right)^2\left(-4x\right)+\left(x+3\right)^2\cdot \:4\\=x^3\left(x+3\right)^2-4x\left(x+3\right)^2+4\left(x+3\right)^2\\=x^5+6x^4+5x^3-20x^2-12x+36$

$c) \left(x-y+5\right)\left(2x-5y-11\right)\\=x\cdot \:2x+x\left(-5y\right)+x\left(-11\right)+\left(-y\right)\cdot \:2x+\left(-y\right)\left(-5y\right)+\left(-y\right)\left(-11\right)+5\cdot \:2x+5\left(-5y\right)+5\left(-11\right)\\=2xx-5xy-11x-2xy+5yy+11y+5\cdot \:2x-5\cdot \:5y-5\cdot \:11\\=-7xy+2x^2-x+5y^2-14y-55$