SUP03-05

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a. \[9a^2 - 4 = (3a)^2 - 2^2 = (3a - 2)(3a+2).\]

b. \[x^2 + 18x + 81 = x^2 + 2\cdot x \cdot 9 + 9^2 = (x+9)^2.\]

c. \[b^2 - 24b + 144 = b^2 - 2\cdot b \cdot 12 + 12^2 = (b-12)^2.\]

d. \[16t^2 + 56t + 49 = (4t)^2 + 2\cdot 4t \cdot 7 + 7^2 = (4t + 7)^2.\]

e. \[t^2 - 1 = t^2 - 1^2 = (t-1)(t+1).\]

f. \[\begin{aligned} (x-2)^2 - 36 &= (x-2)^2 - 6^2& \\ &= \big[(x-2)-6\big]\big[(x-2)+6\big]& \\ &=(x-2-6)(x-2+4)& \\ &= (x-8)(x+2).& \end{aligned}\]

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code : 182