Use either a suitable identity or the distributive property to find each of the following products. (i) (p - 1) (p + 11) Class 8
easyUse either a suitable identity or the distributive property to find each of the following products. (i) (p - 1) (p + 11) Class 8
Question 1.
Use either a suitable identity or the distributive property to find each of the following products.
(i) (p - 1) (p + 11)
(ii) (3a - 9b) (3a + 9b)
(iii) -(2y + 5) (3y + 4)
(iv) (6x + 5y)²
(v) (2x - [latex]\frac{1}{2}[/latex])²
(vi) (7p) × (3x) × (p + 2)
Solution:
(i) (p - 1) (p + 11)
= p(p + 11) - 1 (p + 11)
= p² + 11p - 1p - 11
= p² + 10p - 11
(3a - 9b) (3a + 9b)
= (3a)² - (9b)² = 9a² - 81b²
(iii) -(2y + 5) (3y + 4)
= (-2y - 5) (3y + 4)
= -2y (3y + 4) - 5 (3y + 4)
= -6y² - 8y - 15y - 20
= -6y² - 23y - 20
(iv) (6x + 5y)² = (6x)² + 2 × 6x × 5y + (5y)²
= 36x² + 60xy + 25y²
(v) (2x - [latex]\frac{1}{2}[/latex])² = (2x)² - 2 × 2x × [latex]\frac{1}{2}[/latex] + [latex]\left(\frac{1}{2}\right)^2[/latex]
= 4x² - 2x + [latex]\frac{1}{4}[/latex]
(vi) (7p) × (3r) × (p + 2)
= 21pr × (p + 2)
= 21pr × p + 21pr × 2
= 21p2r + 42pr.