G(x) = -4x+4
h(x)= x³+4x²
find g(x)•h(x)

4x^4-12x^3+16x^2

Step-by-step explanation:

(-4x+4)(x^3+4x^2)

a      b    c      d

using foil method multiply

term a by term c and d

-4x * x^3= -4x^4

-4x * 4x^2= -16x^3

*dont forget to add the exponents, when x is by itself you it always has an imaginary 1

then multiply term b by term c and d

4 * x^3= 4x^3

4 * 4x^2= 16x^2

line up all of your answers from biggest exponent to smallest

-4x^4-16x^3+4x^3+16x^2

we can combine like terms with -16x^3 and 4x^3 becaus ethey have the same exponent value

4x^4-12x^3+16x^2

hello from mrbilldoesmath!

answer:

(7 x + 6 y) (49 x^2 - 42 x y + 36 y^2)

discussion:

the trick is to recognize that 343 = 7^3 and 216 = 6^3 and, in general,

a^3 + b^3 =   (a + b) (a^2 - a b + b^2).

in our case

343x^3+216y^3   =   (7x)^3 + (6y)^3

so take a = 7x and b = 6y in the above equation to get the answer.

you,

mrb