6.4 Factoring by grouping

$ax+ay+bx+by$

$2am+8m+5an+20n$

$a^2{x}^3+4a^2{y}^3+3b{x}^3+12b{y}^3$

$15mx+10nx-6my-4ny$

$40abx-24abxy-35c^{2}x+21c^{2}xy$

When factoring the polynomial $8a^2{b}^4-4b^4+14a^2-7$ in Sample Set A, we grouped together terms1 and 2 and 3 and 4. Could we have grouped together terms1 and 3 and 2 and 4? Try this.
$8a^2{b}^4-4b^4+14a^2-7=$

$2ab+3a+18b+27$

$xy-7x+4y-28$

$xy+x+3y+3$

$mp+3mq+np+3nq$

$ar+4as+5br+20bs$

$14ax-6bx+21ay-9by$

$12mx-6bx+21ay-9by$

$36ak-8ah-27bk+6bh$

$a^2{b}^2+2a^2+3b^2+6$

$3n^2+6n+9m^3+12m$

$8y^4-5y^3+12z^2-10z$

$x^2+4x-3y^2+y$

$x^2-3x+xy-3y$

$2n^2+12n-5mn-30m$

$4pq-7p+3q^2-21$

$8x^2+16xy-5x-10y$

$12s^2-27s-8st+18t$

$15x^2-12x-10xy+8y$

$a^4{b}^4+3a^5{b}^5+2a^2{b}^2+6a^3{b}^3$

$4a^{3}bc-14a^{2}b{c}^3+10ab{c}^2-35b{c}^4$

$5x^2{y}^{3}z+3x^{3}yw-10y^3{z}^2-6wxyz$

$a^3{b}^{2}cd+ab{c}^{2}dx-a^{2}bxy-c{x}^{2}y$

$5m^{10}{n}^{17}{p}^3-m^6{n}^7{p}^4-40m^4{n}^{10}q{t}^2+8pq{t}^2$

( [link] ) Simplify $(x^5{y}^3)(x^{2}y)$ .

( [link] ) Use scientific notation to find the product of $(3\times {10}^{-5})(2\times {10}^2)$ .

( [link] ) Find the domain of the equation $y=\frac{6}{x+5}$ .

( [link] ) Construct the graph of the inequality $y\ge -2$ .

( [link] ) Factor $8a^4{b}^4+12a^3{b}^5-8a^2{b}^3$ .