2010004407
Level:
B
Factor the expression: \(49y^4-4y^2+20y-25\).
\( (7y^2-2y+5)(7y^2+2y-5)\)
\( (7y^2-2y-5)(7y^2+2y-5)\)
\( (7y^2-2y+5)(7y^2+2y+5)\)
\( (7y^2-2y-5)(7y^2+2y+5)\)
Polynomials and fractions
2010004408
Level:
B
Factor the expression: \(81a^4-64a^2-48a-9\).
\( (9a^2-8a-3)(9a^2+8a+3)\)
\( (9a^2-8a+3)(9a^2+8a+3)\)
\( (9a^2-8a-3)(9a^2+8a-3)\)
\( (9a^2-8a+3)(9a^2+8a-3)\)
2010004409
Level:
B
Factor the expression: \( 9x^4y^6 -12x^3y^4 +4x^2y^2\).
\( x^2y^2(3xy^2-2)(3xy^2-2)\)
\( x^2y^2(3xy^2+2)(3xy^2-2)\)
\( x^2y^2(9xy^2-4)(9xy^2-4)\)
\( x^2y^2(9xy^2+2)(9xy^2-4)\)
2010004410
Level:
B
Factor the expression: \( 8a^5b^3-24a^3b^2+18ab\).
\( 2ab(2a^2b-3)(2a^2b-3)\)
\( 2ab(2a^2b-3)(2a^2b+3)\)
\( 2ab(4a^2b-9)(4a^2b-9)\)
\( 2ab(4a^2b-9)(4a^2b+9)\)
2010004411
Level:
B
Factor the expression: \( (4a-1)(2-a) - (12a^2-3a) -(a-3)(4a-1) \).
\( 5(4a-1)(1-a) \)
\( 5(4a-1)(a-1) \)
\( (4a-1)(5a+1) \)
\( (1-4a)(5a+1) \)
2010004412
Level:
B
Factor the expression: \( (8-b)(b-4) - (5b^2-20b)-(b-4)(b-6)\).
\( 7(b-4)(2-b) \)
\( 7(b-4)(b-2) \)
\( (b-4)(7b-2) \)
\( (4-b)(7b-2) \)
2010006603
Level:
B
Assuming \(m\neq 0\), simplify the expression: \[m+n-\frac{m^2-n^2}{m}\]
\( \frac{n(m+n)}m\)
\( \frac{n(m-n)}m\)
\( \frac{mn-n^2}m\)
\( \frac{n^2-mn}m\)
2010006604
Level:
B
Assuming \(p\neq 0\), simplify the expression: \[\frac{p^2-q^2}{p}-(p-q)\]
\( \frac{q(p-q)}p\)
\( \frac{q(p+q)}p\)
\( \frac{q^2+pq}p\)
\( \frac{q^2-pq}p\)
2010006605
Level:
B
Assuming \(a\neq 0\), \(b\neq 0\), \(c\neq 0\), simplify the expression:
\[ \frac{2a-c}{4c} - \frac{3a^2-2ab}{6ac}-\frac{2a}{3c}-\frac{5a-b}{2b}\]
\( \frac{4b^2-8ab-30ac+3bc}{12bc} \)
\( \frac{-4b^2-8ab-30ac+3bc}{12bc} \)
\( \frac{4b^2-8ab-30ac-9bc}{12bc} \)
\( 0\)
2010006606
Level:
B
Assuming \(a\neq 0\), \(b\neq 0\), \(c\neq 0\), simplify the expression:
\[ \frac{5a-c}{6ac} - \frac{2a-3b}{12ab}-\frac{3}{4a}-\frac{2c-3b}{3bc}\]
\( \frac{11ab-5ac-4bc}{6abc} \)
\( \frac{11ab-5ac-5bc}{6abc} \)
\( \frac{-ab-5ac-7bc}{6abc} \)
\( 0\)