Algebra Examples

$4 {(x - 3)}^{3} {(4 x + 7)}^{3} + {(x - 3)}^{2} {(4 x + 7)}^{4}$

Step 1

Factor ${(x - 3)}^{2} {(4 x + 7)}^{3}$ out of $4 {(x - 3)}^{3} {(4 x + 7)}^{3} + {(x - 3)}^{2} {(4 x + 7)}^{4}$ .

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Step 1.1

Factor ${(x - 3)}^{2} {(4 x + 7)}^{3}$ out of $4 {(x - 3)}^{3} {(4 x + 7)}^{3}$ .

${(x - 3)}^{2} {(4 x + 7)}^{3} (4 (x - 3)) + {(x - 3)}^{2} {(4 x + 7)}^{4}$

Step 1.2

Factor ${(x - 3)}^{2} {(4 x + 7)}^{3}$ out of ${(x - 3)}^{2} {(4 x + 7)}^{4}$ .

${(x - 3)}^{2} {(4 x + 7)}^{3} (4 (x - 3)) + {(x - 3)}^{2} {(4 x + 7)}^{3} (4 x + 7)$

Step 1.3

Factor ${(x - 3)}^{2} {(4 x + 7)}^{3}$ out of ${(x - 3)}^{2} {(4 x + 7)}^{3} (4 (x - 3)) + {(x - 3)}^{2} {(4 x + 7)}^{3} (4 x + 7)$ .

${(x - 3)}^{2} {(4 x + 7)}^{3} (4 (x - 3) + 4 x + 7)$

Step 2

Apply the distributive property.

${(x - 3)}^{2} {(4 x + 7)}^{3} (4 x + 4 \cdot - 3 + 4 x + 7)$

Step 3

Multiply $4$ by $- 3$ .

${(x - 3)}^{2} {(4 x + 7)}^{3} (4 x - 12 + 4 x + 7)$

Step 4

Add $4 x$ and $4 x$ .

${(x - 3)}^{2} {(4 x + 7)}^{3} (8 x - 12 + 7)$

Step 5

Add $- 12$ and $7$ .

${(x - 3)}^{2} {(4 x + 7)}^{3} (8 x - 5)$