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Question 1 Simplify the following:   $(a-2)^{2}-a(a+4)$   $(5a-4b)(25a^{2}+20ab+16b^{2})$   $(2m-3)(4m^{2}+9)(2m+3)$   $(a+2b-c)(a+2b+c)$ Question 2 Factorise   \(12x + 32y\)   \(-12a + 24a^{3}\)   \(6d -9r +2t^{5}d -3t^{5}r\)   \(9z -18m +b^{3}z -2b^{3}m\)   \(6j-15v+2yj-5yv\)   \(16a-40k+2za-5zk\)

Question 1 Solve for the unknown variable:   $3^{x-1}-27=0$   $27(4^{x})=(64)3^{x}$   $\sqrt{2x-5}=2-x$   Question 2 Show that $\sqrt{\dfrac{3^{x+1}-3^{x}}{3^{x-1}}+3}$ is equal to $\text{3}$ Hence solve for x$\sqrt{\dfrac{3^{x+1}-3^{x}}{3^{x-1}}+3}=\left(\dfrac{1}{3}\right)^{x-2}$

Question 1 A quadratic pattern is given by \(\; T_{n} = n^{2} + bn + c\). Find the values of \(b\) and \(c\) if the sequence starts with the following terms: $-1 \; ; \; 2 \; ; \; 7 \; ; \; 14 \; ; \; \ldots$ Question 2 The terms \(p; (2p+2); (5p+3)\)… Continue reading Grade 12 Questions on Sequences and Series