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Q3 Expand the brackets in the following expressions. a) 3a(a+3) b) 4r(5-r) C) 6r(t-12) d) 11b(7+b) e) 12z(8+z) f) 7q(9-3q)

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Q3 Expand the brackets in the following expressions. a) 3a(a+3) b) 4r(5-r) C) 6r(t-12) d) 11b(7+b) e) 12z(8+z) f) 7q(9-3q)

Q3 Expand the brackets in the following expressions. a) 3a(a+3) b) 4r(5-r) C) 6r(t-12) d) 11b(7+b) e) 12z(8+z) f) 7q(9-3q)

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YlvaMaster · Tutor for 5 years

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a) \( 3 a(a+3) = 3a^2 + 9a \)<br /><br />## Explanation:<br /><br />### \( 3 a(a+3) = 3a*a + 3a*3 = 3a^2 + 9a \)<br /><br />b) \( 4 r(5-r) = 20r - 4r^2 \)<br /><br />## Explanation:<br /><br />### \( 4 r(5-r) = 4r*5 - 4r*r = 20r - 4r^2 \)<br /><br />c) \( 6 t(t-12) = 6t^2 - 72t \)<br /><br />## Explanation:<br /><br />### \( 6 t(t-12) = 6t*t - 6t*12 = 6t^2 - 72t \)<br /><br />d) \( 11 b(7+b) = 77b + 11b^2 \)<br /><br />## Explanation:<br /><br />### \( 11 b(7+b) = 11b*7 + 11b*b = 77b + 11b^2 \)<br /><br />e) \( 12 z(8+z) = 96z + 12z^2 \)<br /><br />## Explanation:<br /><br />### \( 12 z(8+z) = 12z*8 + 12z*z = 96z + 12z^2 \)<br /><br />f) \( 7 q(9-3 q) = 63q - 21q^2 \)<br /><br />## Explanation:<br /><br />### \( 7 q(9-3 q) = 7q*9 - 7q*3q = 63q - 21q^2 \)

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## Step1:<br />We will apply the distributive property to expand the brackets. The distributive property states that for all real numbers a, b, and c: \(a(b+c) = ab + ac\).<br /><br />## Step2:<br />For each expression, we will multiply the term outside the bracket with each term inside the bracket.
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