Factorise completely: 160* - 72a²b² + 81b⁴
Answers
Answer:
1.1 Factoring x2-12x-160
The first term is, x2 its coefficient is 1 .
The middle term is, -12x its coefficient is -12 .
The last term, "the constant", is -160
Step-1 : Multiply the coefficient of the first term by the constant 1 • -160 = -160
Step-2 : Find two factors of -160 whose sum equals the coefficient of the middle term, which is -12 .
-160 + 1 = -159
-80 + 2 = -78
-40 + 4 = -36
-32 + 5 = -27
-20 + 8 = -12 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -20 and 8
x2 - 20x + 8x - 160
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-20)
Add up the last 2 terms, pulling out common factors :
8 • (x-20)
Step-5 : Add up the four terms of step 4 :
(x+8) • (x-20)
Which is the desired factorization
Equation at the end of step
1
:
(x + 8) • (x - 20) = 0
STEP
2
:
Theory - Roots of a product
2.1 A product of several terms equals zero.
When a product of two or more terms equals zero, then at least one of the terms must be zero.
We shall now solve each term = 0 separately
In other words, we are going to solve as many equations as there are terms in the product
Any solution of term = 0 solves product = 0 as well.
Solving a Single Variable Equation: