คำชื้แอง ไห้นักเรียนแยกตัวประกอบ และเติมคำตอบที่ดูกต้องลงในจองร่าง (ช้อละ 1 คยแนน) 1. \( 30 x^{2} y^{3}+36 x^{3} y^{2}-6 x y^{3}= \) \( \qquad \) 2. \( a^{2}-2 b-5 a^{3}+10 a b \) \( \qquad \) 3. \( 35 m^{2}+18 m-8 \) E. \( \qquad \) 4. \( 6 a^{2}+17 a+12 \) E. \( \qquad \) 5. \( y^{2}-20 y-21 \) 6. \( n^{2}+15 n-54 \) 7. \( 49-4(x+2)^{2} \) \( \pm \) \( \qquad \) 8. \( 180-3 b-b^{2} \)

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. \( 180-3 b-b^{2} = (12-b)(15+b) \) คุณสามารถเติมคำตอบเหล่านี้ลงในแบบฝึกหัดได้เลย!