Factor the expression:

1. 5t⁴u+kt³u²-10t⁴

=   (((5•(t4))•u)+((k•(t3))•(u2)))-(2•5t4)

=   ((5t4 • u) +  t3u2k) -  (2•5t4)

   Pull out like factors :

=    5t4u - 10t4 + t3u2k  =   t3 • (5tu - 10t + u2k)  

=    Factoring    

= 5tu - 10t + u2k

So are final result is :   t3 • (5tu - 10t + u2k)

3. 64w²x+28w⁴x-72w³x

=   (((64•(w2))•x)+((28•(w4))•x))-((23•32w3)•x)

=   (((64•(w2))•x)+((22•7w4)•x))-(23•32w3x)

=   ((26w2 • x) +  (22•7w4x)) -  (23•32w3x)

 Pull out like factors :

=  28w4x - 72w3x + 64w2x  =   4w2x • (7w2 - 18w + 16)

Trying to factor by splitting the middle term :

Factoring  7w2 - 18w + 16

The first term is,  7w2  its coefficient is  7 .

The middle term is,  -18w  its coefficient is  -18 .

The last term, "the constant", is  +16  

Step-1 : Multiply the coefficient of the first term by the constant   7 • 16 = 112  

Step-2 : Find two factors of  112  whose sum equals the coefficient of the middle term, which is   -18 .

-112 + -1 = -113

-56 + -2 = -58

-28 + -4 = -32

-16 = -7 = -23

-14 + -8 = -22

-8 + -14 = -22

So are final result is :   4w2x • (7w2 - 18w + 16)

4. -36y²z³-42y³z² +54y³z⁴

=   ((0-((36•(y2))•(z3)))-((42•(y3))•(z2)))+((2•33y3)•z4)

=   ((0-((36•(y2))•(z3)))-((2•3•7y3)•z2))+(2•33y3z4)

=   ((0 -  ((22•32y2) • z3)) -  (2•3•7y3z2)) +  (2•33y3z4)

 Pull out like factors :

=   54y3z4 - 42y3z2 - 36y2z3  =   6y2z2 • (9yz2 - 7y - 6z)

Trying to factor a multi variable polynomial :

9yz2 - 7y - 6z

So are final result is :   6y2z2 • (9yz2 - 7y - 6z)

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