Algebra Examples

$6 {(x - 5)}^{3} {(7 x + 3)}^{4} + {(x - 5)}^{4} {(7 x + 3)}^{3}$

Step 1

Factor ${(x - 5)}^{3} {(7 x + 3)}^{3}$ out of $6 {(x - 5)}^{3} {(7 x + 3)}^{4} + {(x - 5)}^{4} {(7 x + 3)}^{3}$ .

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Step 1.1

Factor ${(x - 5)}^{3} {(7 x + 3)}^{3}$ out of $6 {(x - 5)}^{3} {(7 x + 3)}^{4}$ .

${(x - 5)}^{3} {(7 x + 3)}^{3} (6 (7 x + 3)) + {(x - 5)}^{4} {(7 x + 3)}^{3}$

Step 1.2

Factor ${(x - 5)}^{3} {(7 x + 3)}^{3}$ out of ${(x - 5)}^{4} {(7 x + 3)}^{3}$ .

${(x - 5)}^{3} {(7 x + 3)}^{3} (6 (7 x + 3)) + {(x - 5)}^{3} {(7 x + 3)}^{3} (x - 5)$

Step 1.3

Factor ${(x - 5)}^{3} {(7 x + 3)}^{3}$ out of ${(x - 5)}^{3} {(7 x + 3)}^{3} (6 (7 x + 3)) + {(x - 5)}^{3} {(7 x + 3)}^{3} (x - 5)$ .

${(x - 5)}^{3} {(7 x + 3)}^{3} (6 (7 x + 3) + x - 5)$

Step 2

Apply the distributive property.

${(x - 5)}^{3} {(7 x + 3)}^{3} (6 (7 x) + 6 \cdot 3 + x - 5)$

Step 3

Multiply $7$ by $6$ .

${(x - 5)}^{3} {(7 x + 3)}^{3} (42 x + 6 \cdot 3 + x - 5)$

Step 4

Multiply $6$ by $3$ .

${(x - 5)}^{3} {(7 x + 3)}^{3} (42 x + 18 + x - 5)$

Step 5

Add $42 x$ and $x$ .

${(x - 5)}^{3} {(7 x + 3)}^{3} (43 x + 18 - 5)$

Step 6

Subtract $5$ from $18$ .

${(x - 5)}^{3} {(7 x + 3)}^{3} (43 x + 13)$