Question

Factor the expression 36a4b10  81a16b20 using the two different techniques listed for Parts 1(a) and 1(b). (a) Factor the given expression using the GCF monomial. (a) Factor the given expression using the GCF monomial. (b) Factor the given expression using the difference of squares.

Answer 1

Answer:

The answer is "$9a^4b^{10}(2+6a^6b^5)(2-6a^6b^5)$"

Step-by-step explanation:

For point a:

$36a^4b^{10} - 81a^{16}b^{20}$ by GCF

Calculating the const terms:$36 \ n \ 81, \ GCF \ is\ 9\times 4 \ n \ 9\times 9$

Calculating the terms  $w\ a: a^4 \ n \ a^{16},\ GCF \ is\ a^4 \ n \ a^4 \times \ a^{12}$

Calculating the terms $w \ b: b^{10}\ n\ b^{20}, \ GCF \ is\ b^{10}\ n \ b^{10} \times b^{10}$

Including the GCFs, $36a^4 b^{10} - 81a^{16}b^{20}$

$=9a^4b^{10}(4 - 9a^{12}b^{10})\\\\4=2^2 n 9a^{12}b^{10}\\\\=(3a^6b^5)^2$

Calculating the difference of squares

$\to A^2 - B^2 = (A+B)(A-B)\\\\\to 4 - 9a^{12}b^{10} \\\\\to (2+3a^6b^5)(2-3a^6b^5)$

substituting

$\to 36a^4b^{10} - 81a^{16}b^{20}\\\\\to 9a^4b^{10}(2+3a^6b^5)(2-3a^6b^5)$

For point b:

Calculating the difference of squares:

$A^2 - B^2 = (A+B)(A-B)\\\\36a^4b^{10}=(6a^2b^5)^2\\\\81a^{16}b^{20}=(9a^8b^{10})^2\\\\36a^4b^{10} - 81a^{16}b^{20}\\\\=(6a^2b^5+9a^8b^{10})(6a^2b^5-9a^8b^{10})\\\\=3a^2b^5(2+6a^6b^5)3a^2b^5(2-6a^6b^5)\\\\=9a^4b^{10}(2+6a^6b^5)(2-6a^6b^5)$