Please answer my question
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Answer:
1.
(i) 12x, 36
= (2 × 6 × x), (6 × 6)
The common factor is 6
(ii) 2y, 22xy
= (2 × y), (2 × 11 × x × y)
The common factors are 2, y
(iii) 14pq, 28p²q²
= (2 × 7 × p × q), (2 × 2 × 7 × p × p × q × q)
The common factors are 2, 7, p, q
(iv) 2x, 3x², 4
= (2 × x), (3 × x × x), (2 × 2)
There are no common factors
(v) 6abc, 24abc², 12a²b
= (6 × a × b × c), (4 × 6 × a × b × c × c), (2 × 6 × a × a × b)
The common factor are 6, a, b
(vi) 16x³, -4x², 32x
= (4 × 4 × x × x × x), (-1 × 4 × x × x), (4 × 8 × x)
The common factors are 4, x
(vii) 10pq, 20qr, 30rp
= (10 × p × q), (2 × 10 × q × r), (3 × 10 × r × p)
The common factor is 10
(viii) 3x²y³, 10x³y², 6x²y²z
= (3 × x × x × y × y × y), (2 × 5 × x × x × x × y × y), (2 × 3 × x × x × y × y × z)
The common factors are x², y²
2.
(i) 7x - 42
= 7(x - 6)
(ii) 6p - 12q
= 6(p - 2q)
(iii) 7a² + 14a
= 7a(a + 2)
(iv) -16z + 20z³
= 4z(-4 + 5z²)
(v) 20l²m + 30alm
= 10lm(2l + 3a)
(vi) 5x²y - 15xy²
= 5xy(x - 3y)
(vii) 10a² - 15b² + 20c²
= 5(2a² - 3b² + 4c²)
(viii) -4a² + 4ab - 4ca
= 4a(-a + b - c)
(ix) x²yz + xy²z + xyz²
= xyz(x + y + z)
(x) ax²y + bxy² + cxyz
= xy(ax + by + cz)
3.
(i) x² + xy + 8x + 8y
= x(x + y) + 8(x + y)
= (x + y)(x + 8)
(ii) 15xy - 6x + 5y - 2
= 15xy + 5y - 6x - 2
= 5y(3x + 1) - 2(3x + 1)
= (3x + 1)(5y - 2)