Question

Helpp es de multiplicar los polinomios ​

Answer 1

Respuesta:

1) 18a²b-12ab²+27a-18b

2) -7x³y²-7xy⁴-2x⁴y-2x²y³

3) 4p²+14pq-8q²+5p+20q

4) 2m²+3mn-5n²-m+n

Explicación paso a paso:

1)

$\left(6ab+9\right)\left(3a-2b\right)\\=6ab\cdot \:3a+6ab\left(-2b\right)+9\cdot \:3a+9\left(-2b\right)\\=6\cdot \:3aab-6\cdot \:2abb+9\cdot \:3a-9\cdot \:2b$

• $6\cdot \:3aab=18a^2b$
• $6\cdot \:2abb=12ab^2$
• $9\cdot \:3a=27a$
• $9\cdot \:2b=18b$

$=18a^2b-12ab^2+27a-18b$

2)

$\left(-7xy^2-2x^2y\right)\left(x^2+y^2\right)\\=\left(-7xy^2\right)x^2+\left(-7xy^2\right)y^2+\left(-2x^2y\right)x^2+\left(-2x^2y\right)y^2\\=-7x^2xy^2-7xy^2y^2-2x^2x^2y-2x^2y^2y$

• $7x^2xy^2=7x^3y^2$
• $7xy^2y^2=7xy^4$
• $2x^2x^2y=2x^4y$
• $2x^2y^2y=2x^2y^3$

$=-7x^3y^2-7xy^4-2x^4y-2x^2y^3$

3)

$\left(4p-2q+5\right)\left(p+4q\right)\\=4pp+4p\cdot \:4q+\left(-2q\right)p+\left(-2q\right)\cdot \:4q+5p+5\cdot \:4q\\=4pp+4\cdot \:4pq-2pq-2\cdot \:4qq+5p+5\cdot \:4q$

• $4pp=4p^2$
• $4\cdot \:4pq=16pq$
• $2\cdot \:4qq=8q^2$
• $5\cdot \:4q=20q$

$=4p^2+16pq-2pq-8q^2+5p+20q\\=4p^2+14pq-8q^2+5p+20q$

4)

$\left(2m+5n-1\right)\left(m-n\right)\\=2mm+2m\left(-n\right)+5nm+5n\left(-n\right)+\left(-1\right)m+\left(-1\right)\left(-n\right)\\=2mm-2mn+5mn-5nn-1\cdot \:m+1\cdot \:n\\=2mm+3mn-5nn-1\cdot \:m+1\cdot \:n$

• $2mm=2m^2$
• $5nn=5n^2$
• $1\cdot \:m=m$
• $1\cdot \:n=n$

$=2m^2+3mn-5n^2-m+n$