Expand the following using both Identity 1B and by applying the distributive property (i) (b - 6)² (ii)(-2a + 3)² Class 8
easyExpand the following using both Identity 1B and by applying the distributive property (i) (b - 6)² (ii)(-2a + 3)² Class 8
Question 1.
Expand the following using both Identity 1B and by applying the distributive property Class 8
(i) (b - 6)²
(ii) (-2a + 3)²
(iii) (7y - [latex]\frac{3}{4 z}[/latex])²
Solution:
(i) (b - 6)² = b² - 2 × b × 6 × b²
= b² - 12b + 36
or (b - 6)² = (b - 6) (b - 6)
= b (b - 6) - 6 (b - 6)
= b² - 6b - 6b + 36
= b² - 12b + 36
(ii) (—2a + 3)² = (3 - 2a)²
= 3² - 2 × 3 × 2a + (2a)²
= 9 - 12a + 4a²
or (-2a + 3)² = (-2a + 3) (-2a + 3)
= —2a (—2a + 3) + 3 (—2a + 3)
= 4a2 — 6a — 6a + 9
= 4a2 - 12a + 9
(iii) (7y - [latex]\frac{3}{4 z}[/latex])² = (7y)² - 2 × 7y × [latex]\frac{3}{4 z}[/latex] + [latex]\left(\frac{3}{4 z}\right)^2[/latex]
= 49y² - [latex]\frac{21 y}{2 z}+\frac{9}{16 z^2}[/latex]
or [latex]\left(7 y-\frac{3}{4 z}\right)\left(7 y-\frac{3}{4 z}\right)[/latex]
= 7y(7y - [latex]\frac{3}{4 z}[/latex]) - [latex]\frac{3}{4 z}[/latex](7y - [latex]\frac{3}{4 z}[/latex])
= 49y² - [latex]\frac{21 y}{4 z}-\frac{21 y}{4 z}+\frac{9}{16 z^2}[/latex]
= 49y² - [latex]\frac{21 y}{2 z}+\frac{9}{16 z^2}[/latex]