Problem 1 :
4x + 10
Problem 2 :
5y - 15
Problem 3 :
7p^{2} + 21p
Problem 4 :
3x + 9xy
Problem 5 :
39pq^{2} - 52p^{2}q
Problem 6 :
60a^{2}b^{3} + 75ab^{6}
Problem 7 :
y^{2} - 25
Problem 8 :
9x^{2} - 49
Problem 9 :
16a^{2} - 25b^{2}
Problem 10 :
1. Answer :
= 4x + 10
The largest common divisor for 4x and 10 is 2.
Divide 4x and 10 by 2.
Write the quotients 2x and 5 inside the parentheses and multiply by the largest common divisor 2.
= 2(2x + 5)
2. Answer :
= 5y - 15
The largest common divisor for 5y and 15 is 5.
Divide 5y and 15 by 5.
Write the quotients y and 3 inside the parentheses and multiply by the largest common divisor 5.
3. Answer :
= 7p^{2} + 21p
The largest common divisor for 7p^{2} and 21p.
Divide 7p^{2} and 21p is 7p.
Write the quotients p and 3 inside the parentheses and multiply by the largest common divisor 7p.
= 7p(p + 3)
4. Answer :
= 3x + 9xy
The largest common divisor for 3x and 9xy is 3x.
Divide 3x and 9xy is 3x.
Write the quotients 1 and 3x inside the parentheses and multiply by the largest common divisor 2y.
= 3x(1 + 2y)
5. Answer :
= 39pq^{2} - 52p^{2}q
The largest common divisor for 39 and 52 is 13.
The largest common divisor for p and p^{2} is p.
The largest common divisor for q^{2} and q is q.
Therefore, the largest common divisor of 39pq^{2} and 52p^{2}q is 13pq.
Divide 39pq^{2} and 52p^{2}q by 13pq.
Write the quotients 3q and 4p inside the parentheses and multiply by the largest common divisor 13pq.
= 13pq(3q + 4p)
6. Answer :
= 60a^{2}b^{3} + 75ab^{6}
The largest common divisor for 60 and 75 is 15.
The largest common divisor for a^{2} and a is a.
The largest common divisor for b^{3} and b^{6} is b^{3}.
Therefore, the largest common divisor of 60a^{2}b^{3} and 75ab^{6} is 15ab^{3}.
Divide 60a^{2}a^{3} and 75ab^{6} by 15ab^{3}.
Write the quotients 4a and 5b^{3} inside the parentheses and multiply by the largest common divisor 15ab^{3}.
= 15ab^{3}(4a + 5b^{3})
7. Answer :
The given binomial (y^{2} - 25) can be written as a difference of two squares. Then, we can factor it using the following algebraic identity.
a^{2} - a^{2} = (a + b)(a - b)
= y^{2} - 25
= y^{2} - 5^{2}
= (y + 5)(y - 5)
8. Answer :
= 9x^{2} - 49
= 3^{2}x^{2} - 7^{2}
= (3x)^{2} - 7^{2}
= (3x + 7)(3x - 7)
9. Answer :
= 16a^{2} - 25b^{2}
= 4^{2}a^{2} - 5^{2}b^{2}
= (4a)^{2} - (5b)^{2}
= (4a + 5b)(4a - 5b)
10. Answer :
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