Question

2. Find each of the following products of monomials. (a) (3x?) (10x) (b) (-2x)(-9x) (c) (4x+y)(8x*y) (d) (5x) (e) (-41)(-151") 2 (f) (7x)(5xy^) ** | (12x) (h) (2xP)(5x)(-6x4)

Answer 1

In order to solve the products between the followings monomials you take into account that the multiplication is in between coefficients, and also you take into account that it is necessary to multiply the involved signs.

a)

`(3x^3)(10x^4)=(3)(10)x^{^(3+4)}=30x^7`

when the product is between the same variable but different exponents, you sum the exponents

b)

`(-2x^5)(-9x)=(-2)(-9)x^(5+1)=18x^6`

where you have used that minus multiplied by minus is equal to positive

c)

`(4x^2y)(8x^5y^3)=(4)(8)x^(2+5)y^(1+3)=32x^7y^4`

where you sum the exponents of x and y

d)

`(5x^4)^2=(5)^2(x^4)^2=25x^(4\cdot2)=25x^8`

In the case in which you have a variable with an exponent, power to another exponent, these exponents must be multiplied. The coeeficient also has to be exponentiated

e)

`(-4t^2)(-15t^5)=(-4)(-15)t^(2+5)=60t^7`

f)

`(7x)(5xy^4)=35x^2y^4`

g)

`((2)/(3)x^4)(12x)=(2\cdot12)/(3)x^5=8x^5`

f)

`(2x^2)(5x)(-6x^4)=(2)(5)(-6)x^(2+1+4)=-60x^7`

where you multiply all coefficientes and signs, and sum the exponents of x