1. 12x + 6 2. 6a - 11 3. 3x² - 1 4. m + 3 5. y + 4
2x + 3 3a + 2 x + 4 m - 6 y + 7
Answers:
1. 24x² + 48x + 18
2. 18a² - 19a - 22
3. 3x³ + 12x² - x - 4
4. m² - 3m - 18
5. y² + 11y + 28
Solutions:
1. ( 12x + 6 ) ( 2x + 3 )
= 12x(2x + 3) + 6(2x+3)
= (12x × 2x) + (12x × 3) + (6 × 2x) + (6 × 3)
= 24x² + 36x + 12x + 18
= 24x² + 48x + 18
2. (6a - 11) (3a + 2)
= 6a(3a + 2) - 11(3a + 2)
= (6a × 3a) + (6a × 2) - (11 × 3a) - (11 × 2)
= 18a² + 12a - 33a - 22
3. (3x² - 1) (x + 4)
= 3x²(x + 4) - 1(x + 4)
= 3x³ + 12x² - x + 4
4. (m + 3) (m - 6)
= m(m - 6) + 3(m - 6)
= m² - 6m + 3m - 18
= m² - 3m - 18
5. (y + 4) (y + 7)
= y(y + 7) + 4(y + 7)
= y² + 7y + 4y + 28
= y² + 11y + 28
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Answers & Comments
1. 12x + 6 2. 6a - 11 3. 3x² - 1 4. m + 3 5. y + 4
2x + 3 3a + 2 x + 4 m - 6 y + 7
Answers:
1. 24x² + 48x + 18
2. 18a² - 19a - 22
3. 3x³ + 12x² - x - 4
4. m² - 3m - 18
5. y² + 11y + 28
Solutions:
1. ( 12x + 6 ) ( 2x + 3 )
= 12x(2x + 3) + 6(2x+3)
= (12x × 2x) + (12x × 3) + (6 × 2x) + (6 × 3)
= 24x² + 36x + 12x + 18
= 24x² + 48x + 18
2. (6a - 11) (3a + 2)
= 6a(3a + 2) - 11(3a + 2)
= (6a × 3a) + (6a × 2) - (11 × 3a) - (11 × 2)
= 18a² + 12a - 33a - 22
3. (3x² - 1) (x + 4)
= 3x²(x + 4) - 1(x + 4)
= 3x³ + 12x² - x + 4
4. (m + 3) (m - 6)
= m(m - 6) + 3(m - 6)
= m² - 6m + 3m - 18
= m² - 3m - 18
5. (y + 4) (y + 7)
= y(y + 7) + 4(y + 7)
= y² + 7y + 4y + 28
= y² + 11y + 28