Question

simplify and evaluate the following expression:
a) $44x^{7}y^{3}z - 143x^{2}z^{5}+132x^{4}y^{7}z^{6}$
b) $8x^{3}-6x^{2}+20x - 15$

Explanation:

Step1: Find GCF for part a

Find the greatest - common factor of the coefficients 44, 143, and 132. The GCF of 44, 143, and 132 is 11. And there are no common variables among all three terms other than 1. So, \(44x^{7}y^{3}z−143x^{2}z^{5}+132x^{4}y^{7}z^{6}=11(4x^{7}y^{3}z - 13x^{2}z^{5}+12x^{4}y^{7}z^{6})\). Since no values for \(x\), \(y\), and \(z\) are given, we can't evaluate it further.

Step2: Group terms for part b

Group the terms of \(8x^{3}-6x^{2}+20x - 15\) as \((8x^{3}-6x^{2})+(20x - 15)\).

Step3: Factor out GCF from each group

Factor out the GCF from each group. From \(8x^{3}-6x^{2}\), the GCF is \(2x^{2}\), so \(8x^{3}-6x^{2}=2x^{2}(4x - 3)\). From \(20x - 15\), the GCF is 5, so \(20x - 15 = 5(4x - 3)\).

Step4: Combine the factored - out terms

\((8x^{3}-6x^{2})+(20x - 15)=2x^{2}(4x - 3)+5(4x - 3)=(4x - 3)(2x^{2}+5)\). Since no value for \(x\) is given, we can't evaluate it further.

Answer:

a) \(11(4x^{7}y^{3}z - 13x^{2}z^{5}+12x^{4}y^{7}z^{6})\)
b) \((4x - 3)(2x^{2}+5)\)