Question

① $12x^{10} + 9x^{10} =$
② $-54xy + 12x^2 - 6x$

Explanation:

Problem ①

Step1: Identify the GCF of coefficients and variables.

For the terms \(12x^{10}\) and \(9x^{10}\), the GCF of 12 and 9 is 3, and the GCF of \(x^{10}\) and \(x^{10}\) is \(x^{10}\).

Step2: Factor out the GCF.

Factor out \(3x^{10}\) from \(12x^{10}+9x^{10}\):
\(12x^{10}+9x^{10}=3x^{10}(4 + 3)\)

Step3: Simplify the expression inside the parentheses.

Simplify \(4 + 3\) to get 7:
\(3x^{10}\times7 = 21x^{10}\)

Step1: Identify the GCF of coefficients and variables.

For the terms \(-54xy\), \(12x^{2}\), and \(-6x\), the GCF of -54, 12, and -6 is -6, and the GCF of \(xy\), \(x^{2}\), and \(x\) is \(x\).

Step2: Factor out the GCF.

Factor out \(-6x\) from \(-54xy + 12x^{2}-6x\):
\(-54xy + 12x^{2}-6x=-6x(9y - 2x + 1)\)

Answer:

\(21x^{10}\)

Problem ②