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Chapter 7

Elementary Algebra · 323 exercises

Problem 223

Factor. \(49 x^{2}-28 x y+4 y^{2}\)

5 step solution

Problem 224

Factor. \(25 r^{2}-60 r s+36 s^{2}\)

5 step solution

Problem 226

Factor. \(100 y^{2}-20 y+1\)

6 step solution

Problem 228

Factor. \(100 x^{2}-25 x+1\)

3 step solution

Problem 229

Factor. \(10 k^{2}+80 k+160\)

4 step solution

Problem 230

Factor. \(64 x^{2}-96 x+36\)

5 step solution

Problem 231

Factor. \(75 u^{3}-30 u^{2} v+3 u v^{2}\)

4 step solution

Problem 232

Factor. \(90 p^{3}+300 p^{2} q+250 p q^{2}\)

4 step solution

Problem 233

Factor. \(x^{2}-16\)

5 step solution

Problem 234

Factor. \(n^{2}-9\)

4 step solution

Problem 235

Factor. \(25 v^{2}-1\)

3 step solution

Problem 236

Factor. \(169 q^{2}-1\)

4 step solution

Problem 237

Factor. \(121 x^{2}-144 y^{2}\)

4 step solution

Problem 238

Factor. \(49 x^{2}-81 y^{2}\)

3 step solution

Problem 239

Factor. \(169 c^{2}-36 d^{2}\)

3 step solution

Problem 240

Factor. \(36 p^{2}-49 q^{2}\)

3 step solution

Problem 241

Factor. \(4-49 x^{2}\)

3 step solution

Problem 242

Factor. \(121-25 s^{2}\)

3 step solution

Problem 243

Factor. \(16 z^{4}-1\)

4 step solution

Problem 244

Factor. \(m^{4}-n^{4}\)

4 step solution

Problem 245

Factor. \(5 q^{2}-45\)

4 step solution

Problem 246

Factor. \(98 r^{3}-72 r\)

3 step solution

Problem 249

Factor. \(x^{3}+125\)

3 step solution

Problem 251

Factor. \(z^{3}-27\)

3 step solution

Problem 252

Factor. \(v^{3}-216\)

4 step solution

Problem 253

Factor. \(8-343 t^{3}\)

4 step solution

Problem 254

Factor. \(125-27 w^{3}\)

5 step solution

Problem 255

Factor. . \(8 y^{3}-125 z^{3}\)

6 step solution

Problem 256

Factor. \(27 x^{3}-64 y^{3}\)

5 step solution

Problem 258

Factor. \(6 x^{3}-48 y^{3}\)

5 step solution

Problem 260

Factor. \(-2 x^{3}-16 y^{3}\)

4 step solution

Problem 261

Factor. \(64 a^{2}-25\)

3 step solution

Problem 262

Factor. \(121 x^{2}-144\)

4 step solution

Problem 264

Factor. \(4 p^{2}-100\)

4 step solution

Problem 265

Factor. \(16 x^{2}-72 x+81\)

4 step solution

Problem 266

Factor. \(36 y^{2}+12 y+1\)

4 step solution

Problem 267

Factor. \(8 p^{2}+2\)

3 step solution

Problem 270

Factor. \(27 u^{3}+1000\)

5 step solution

Problem 271

Factor. \(45 n^{2}+60 n+20\)

6 step solution

Problem 272

Factor. \(48 q^{3}-24 q^{2}+3 q\)

2 step solution

Problem 273

Sue and Alan are planning to put a 15 foot square swimming pool in their backyard. They will surround the pool with a tiled deck, the same width on all sides. If the width of the deck is \(w\), the total area of the pool and deck is given by the trinomial \(4 w^{2}+60 w+225\). Factor the trinomial.

5 step solution

Problem 274

The height a twelve foot ladder can reach up the side of a building if the ladder's base is \(b\) feet from the building is the square root of the binomial \(144-b^{2}\). Factor the binomial.

3 step solution

Problem 277

Explain why \(n^{2}+25 \neq(n+5)^{2}\). Use algebra, words, or pictures.

4 step solution

Problem 278

Maribel factored \(y^{2}-30 y+81\) as \((y-9)^{2}\). Was she right or wrong? How do you know?

5 step solution

Problem 279

Factor completely. \(10 x^{4}+35 x^{3}\)

3 step solution

Problem 280

Factor completely. \(18 p^{6}+24 p^{3}\)

4 step solution

Problem 281

Factor completely. \(y^{2}+10 y-39\)

6 step solution

Problem 282

Factor completely. \(b^{2}-17 b+60\)

5 step solution

Problem 283

Factor completely. \(2 n^{2}+13 n-7\)

6 step solution

Problem 284

Factor completely. \(8 x^{2}-9 x-3\)

7 step solution

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