So I’m going to start by drawing our usual x and x on my left and on our right, we look at the factors of nine. But I want to make this into a perfect square, how about 3 and 3? 3 times 3 makes 9, and at 3 plus 3 makes 6. So I’m going to use 3 and 3. And if you cross multiply you get 3x cross multiply you get 3x. And 3x plus 3x is 6x which is what we have in the middle.
So that’s the right combination so we’ve got x plus 3 times x plus 3 which is x plus 3 squared because we have two of the same kind, ok? That’s it and that’s the perfect square, all right?
So very simple. Fifteen! okay! x and x, four. I think this is an easy one four is two times two so I’m gonna put two and two. I’m not gonna worry about any negatives because they’re all positive. So cross multiply, 2x. Cross multiply, 2x. 2x plus 2x is 4x. So it’s going to be x plus 2, x plus 2.
I forgot to say that’s the same as that isn’t it? that’s why I know that that’s the correct combination. So we’ve got two of the same kind it’s simply going to be x plus 2 squared, so make sure you can simplify it like this, okay? And that’s the answer.
Algebra Algebraic Fractions Arc Binomial Expansion Capacity Common Difference Common Ratio Differentiation Divisibility Proof Double-Angle Formula Equation Exponent Exponential Function Factorials Factorise Functions Geometric Sequence Geometric Series Index Laws Inequality Integration Kinematics Length Conversion Logarithm Logarithmic Functions Mass Conversion Mathematical Induction Measurement Perfect Square Perimeter Prime Factorisation Probability Proof Pythagoras Theorem Quadratic Quadratic Factorise Rational Functions Sequence Sketching Graphs Surds Time Transformation Trigonometric Functions Trigonometric Properties Volume