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1. \( 30 x^{2} y^{3}+36 x^{3} y^{2}-6 x y^{3} = 6xy^{2}(5xy+6x^{2}-y) \)
2. \( a^{2}-2 b-5 a^{3}+10 a b = -(a^{2}-2b)(5a-1) \)
3. \( 35 m^{2}+18 m-8 = (5m+4)(7m-2) \)
4. \( 6 a^{2}+17 a+12 = (2a+3)(3a+4) \)
5. \( y^{2}-20 y-21 = (y-21)(y+1) \)
6. \( n^{2}+15 n-54 = (n-3)(n+18) \)
7. \( 49-4(x+2)^{2} = (3-2x)(11+2x) \)
8. \( 180-3 b-b^{2} = (12-b)(15+b) \)
Solución
Factor the expression by following steps:
- step0: Factor:
\(6a^{2}+17a+12\)
- step1: Rewrite the expression:
\(6a^{2}+\left(8+9\right)a+12\)
- step2: Calculate:
\(6a^{2}+8a+9a+12\)
- step3: Rewrite the expression:
\(2a\times 3a+2a\times 4+3\times 3a+3\times 4\)
- step4: Factor the expression:
\(2a\left(3a+4\right)+3\left(3a+4\right)\)
- step5: Factor the expression:
\(\left(2a+3\right)\left(3a+4\right)\)
Factor the expression \( 180-3 b-b^{2} \).
Factor the expression by following steps:
- step0: Factor:
\(180-3b-b^{2}\)
- step1: Rewrite the expression:
\(180+\left(12-15\right)b-b^{2}\)
- step2: Calculate:
\(180+12b-15b-b^{2}\)
- step3: Rewrite the expression:
\(12\times 15+12b-b\times 15-b\times b\)
- step4: Factor the expression:
\(12\left(15+b\right)-b\left(15+b\right)\)
- step5: Factor the expression:
\(\left(12-b\right)\left(15+b\right)\)
Factor the expression \( n^{2}+15 n-54 \).
Factor the expression by following steps:
- step0: Factor:
\(n^{2}+15n-54\)
- step1: Rewrite the expression:
\(n^{2}+\left(18-3\right)n-54\)
- step2: Calculate:
\(n^{2}+18n-3n-54\)
- step3: Rewrite the expression:
\(n\times n+n\times 18-3n-3\times 18\)
- step4: Factor the expression:
\(n\left(n+18\right)-3\left(n+18\right)\)
- step5: Factor the expression:
\(\left(n-3\right)\left(n+18\right)\)
Factor the expression \( 30 x^{2} y^{3}+36 x^{3} y^{2}-6 x y^{3} \).
Factor the expression by following steps:
- step0: Factor:
\(30x^{2}y^{3}+36x^{3}y^{2}-6xy^{3}\)
- step1: Rewrite the expression:
\(6xy^{2}\times 5xy+6xy^{2}\times 6x^{2}-6xy^{2}\times y\)
- step2: Factor the expression:
\(6xy^{2}\left(5xy+6x^{2}-y\right)\)
Factor the expression \( a^{2}-2 b-5 a^{3}+10 a b \).
Factor the expression by following steps:
- step0: Factor:
\(a^{2}-2b-5a^{3}+10ab\)
- step1: Calculate:
\(-5a^{3}+a^{2}+10ba-2b\)
- step2: Rewrite the expression:
\(-a^{2}\times 5a+a^{2}+2b\times 5a-2b\)
- step3: Factor the expression:
\(-a^{2}\left(5a-1\right)+2b\left(5a-1\right)\)
- step4: Factor the expression:
\(\left(-a^{2}+2b\right)\left(5a-1\right)\)
- step5: Factor the expression:
\(-\left(a^{2}-2b\right)\left(5a-1\right)\)
Factor the expression \( y^{2}-20 y-21 \).
Factor the expression by following steps:
- step0: Factor:
\(y^{2}-20y-21\)
- step1: Rewrite the expression:
\(y^{2}+\left(1-21\right)y-21\)
- step2: Calculate:
\(y^{2}+y-21y-21\)
- step3: Rewrite the expression:
\(y\times y+y-21y-21\)
- step4: Factor the expression:
\(y\left(y+1\right)-21\left(y+1\right)\)
- step5: Factor the expression:
\(\left(y-21\right)\left(y+1\right)\)
Factor the expression \( 35 m^{2}+18 m-8 \).
Factor the expression by following steps:
- step0: Factor:
\(35m^{2}+18m-8\)
- step1: Rewrite the expression:
\(35m^{2}+\left(-10+28\right)m-8\)
- step2: Calculate:
\(35m^{2}-10m+28m-8\)
- step3: Rewrite the expression:
\(5m\times 7m-5m\times 2+4\times 7m-4\times 2\)
- step4: Factor the expression:
\(5m\left(7m-2\right)+4\left(7m-2\right)\)
- step5: Factor the expression:
\(\left(5m+4\right)\left(7m-2\right)\)
Factor the expression \( 49-4(x+2)^{2 \).
Factor the expression by following steps:
- step0: Factor:
\(49-4\left(x+2\right)^{2}\)
- step1: Factor the expression:
\(\left(7-2\left(x+2\right)\right)\left(7+2\left(x+2\right)\right)\)
- step2: Calculate:
\(\left(3-2x\right)\left(11+2x\right)\)
นี่คือการแยกตัวประกอบของแต่ละสมการที่ให้มา:
1. \( 30 x^{2} y^{3}+36 x^{3} y^{2}-6 x y^{3} = 6xy^{2}(5xy+6x^{2}-y) \)
2. \( a^{2}-2 b-5 a^{3}+10 a b = -(a^{2}-2b)(5a-1) \)
3. \( 35 m^{2}+18 m-8 = (5m+4)(7m-2) \)
4. \( 6 a^{2}+17 a+12 = (2a+3)(3a+4) \)
5. \( y^{2}-20 y-21 = (y-21)(y+1) \)
6. \( n^{2}+15 n-54 = (n-3)(n+18) \)
7. \( 49-4(x+2)^{2} = (3-2x)(11+2x) \)
8. \( 180-3 b-b^{2} = (12-b)(15+b) \)
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Respondido por UpStudy AI y revisado por un tutor profesional

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