Expanding, Factors,simplifying Algebra Expanding, Factors,simplifying

Do now 𝑎−𝑏−𝑐 2 −𝑥 4𝑥−1 2 −𝑥(2+3𝑥) 𝑥 2 +3𝑥+2 3𝑥 2 −𝑥−2 Expand and Simplify 𝑎−𝑏−𝑐 2 −𝑥 4𝑥−1 2 −𝑥(2+3𝑥) Factorise 𝑥 2 +3𝑥+2 3𝑥 2 −𝑥−2

Factorising polynomials 8𝑥 2 +6𝑥−35 𝑤𝑥+𝑢𝑥+𝑤𝑦+𝑢𝑦

Rational expressions (3 𝑥 2 𝑦) 3 ×4 (𝑥𝑦) 4 36 𝑥 5 𝑦 7 𝑝 𝑥 2 + 𝑞 𝑥𝑦

𝑥 2 −𝑥−12 𝑥 2 −16 𝑥 2 +𝑥−6 𝑥 2 −𝑥 × 𝑥 2 −1 2𝑥−4

Practice ESA page 143 onwards Theta page 20 onwards Theta page 9 onwards (Language practice)

Do now 𝑥 2 −8𝑥+7 𝑥−1 𝑖𝑓 𝑥=2, 𝑥−2 𝑥+2 = 𝑓 𝑥 = 𝑥 2 +3𝑥−1, 𝑓𝑖𝑛𝑑 𝑓(−1) State the operation you would use and give the end result (Expand, Factorise, Solve, Evaluate, Simplify) 𝑥 2 −8𝑥+7 𝑥−1 (𝑥−3) 2 =16 𝑖𝑓 𝑥=2, 𝑥−2 𝑥+2 = 𝑓 𝑥 = 𝑥 2 +3𝑥−1, 𝑓𝑖𝑛𝑑 𝑓(−1)

Do now The roots of an equation are 𝑥 1 = 3 2 𝑎𝑛𝑑 𝑥 2 =− 6 7 . show this equation in terms of 𝑎 𝑥 2 +𝑏𝑥+𝑐=0. 𝑥 2 +8𝑥+100= 𝑥 2 +8𝑥+64+___________=0 so 𝑥 2 +8𝑥+100=(𝑥+4)+________

Write with a positive index: Negative power means take the reciprocal. Negative power means take the reciprocal. Simplify.

Negative power means take the reciprocal. 8.02B Evaluate: Negative power means take the reciprocal. Work out the power.

Negative power means take the reciprocal. 8.02B Evaluate: Negative power means take the reciprocal. Work out the power. Work out. Alternatively: Write 0.5 as a fraction. Negative power means take the reciprocal. Work out.

Negative power means take the reciprocal. Write as a fraction. Negative power means take the reciprocal. The reciprocal of 2 3 is Work out the power.

Answer using positive indices only 8.03 Simplify (a) (b) Answer using positive indices only (a) Multiply the numbers.

The denominator of 5 means a 5th root.

The denominator of 3 means a 3rd root. 8.04B The denominator of 3 means a 3rd root. Evaluate.

The 4th root means there is a 4 in the denominator of the power. 8.04C The 4th root means there is a 4 in the denominator of the power.

Raise each term to the power of . 8.04D Raise each term to the power of . 1 2 As a power of means a square root, take the square root of 64. 1 2

Multiply for the power of x. 8.04D Multiply for the power of x.

Evaluate the fractional power (a square root). Break up the fractional power into two powers to get a simple root raised to a simple power. Evaluate the fractional power (a square root). Evaluate the power 3.

Write the square root as power . 8.04F Write the square root as power . 1 2 A power of a power means multiply the powers.

The negative sign in the power means a reciprocal. The 3 in the denominator of the power means a cube root.

Negative power. Write term in the denominator of a fraction. 8.05B Evaluate (a) (b) (a) Negative power. Write term in the denominator of a fraction. Write the term in the denominator as a root. Evaluate the root.

Negative power. Take reciprocal of fraction. 8.05B Evaluate (a) (b) (b) Negative power. Take reciprocal of fraction. Write the term in the denominator of the power as a root. Evaluate the root. Evaluate the power.

Note that 4 = 22. Therefore replace 4 by its equivalent 22. 8.06 Simplify Note that 4 = 22. Therefore replace 4 by its equivalent 22. Multiply out the power of a power. Subtract powers to divide.

Practice Theta pages 16 and 76